Using diaries for many weeks, a study on the lifestyles of visually impaired students was conducted. The students kept track of many lifestyle variables including how many hours of sleep obtained on a typical day. Researchers found that visually impaired students averaged 8.82 hours of sleep, with a standard deviation of 2.12 hours. Assume that the number of hours of sleep for these visually impaired students is normally distributed.

(a)  What is the probability that a visually impaired student gets at most 6.2 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer.

Answer: ____%

(b)  What is the probability that a visually impaired student gets between 6.6 and 10.28 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer.

Answer: _____%

(c)  What is the probability that a visually impaired student gets at least 7.3 hours of sleep? Express your answer as a percent rounded to 2 decimal places. e.g. 1.23% Do not include the % symbol in your answer.

Answer: ______%

(d)  What is the sleep time that cuts off the top 38.4% of sleep hours? Round your answer to 2 decimal places.

Answer: _____hours

(e)  If 100 visually impaired students were studied, how many students would you expect to have sleep times of more than 10.28 hours? Round to the nearest whole number.

Answer: _____students

(f)  A school district wants to give additional assistance to visually impaired students with sleep times at the first quartile and lower. What would be the maximum sleep time to be recommended for additional assistance? Round your answer to 2 decimal places.

Answer: ______hours

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 68.0 kg and standard deviation σ = 7.8 kg. Suppose a doe that weighs less than 59 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2350 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 60 does should be more than 65 kg. If the average weight is less than 65 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 60 does is less than 65 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x < 69.8 kg for 60 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 60 does in December, and the average weight was

x = 69.8 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.   

Since the sample average is above the mean, it is quite likely that the doe population is undernourished

.Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Piotr Banasiewicz is a self-employed plumber who offers a 24-hour emergency service. For most of the year, calls arrive randomly at a rate of six a day. The time he takes to travel to a call and do the repair is randomly distributed with a mean of 90 minutes. Forecasts for February suggest cold weather and last time this happened Piotr received emergency calls at a rate of 18 a day. Because of repeat business, Piotr is anxious not to lose a customer and wants the average waiting time to be no longer in February than during a normal month. How many assistants should he employ to achieve this? • Assume a Single-Server model. • Ignore the stated Repair Time of 90 minutes. Instead, assume theRepair Time is 80 minutes. • Ignore the Arrival Rate of 6 per day. Instead, assume the Arrival Rateis 7 per day • In addition to the questions in the stated problem, determine the following: o Average server utilization o Average number of customers in the queue (Lq) o Average number of customers in the system (L) o Average waiting time in the queue (Wq) – express in days, hoursand minutes. o Average waiting time in the system (W) ) – express in days, hoursand minutes. o Probability there is 0 units in the system (P0) o Probability of "n" units in system with n=0 to up to n=20. o Probability of more than "n" units in system with n=0 to up to n=20. • Ignore the “How many assistants should he employ to achieve this?” question. • Instead, determine what the minimum Service Rate in customers per day should be for February, in order to maintain or improve the average waiting time (Wq) for the rest of the year. Please give step by step instructions on excel with formulas on how to solve.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 55.0 kg and standard deviation σ = 8.2 kg. Suppose a doe that weighs less than 46 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2600 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 52 kg. If the average weight is less than 52 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 70 does is less than 52 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 56.9 kg for 70 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was

x

= 56.9 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. Since the sample average is below the mean, it is quite likely that the doe population is undernourished.     Since the sample average is above the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 58.0 kg and standard deviation σ = 6.4 kg. Suppose a doe that weighs less than 49 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2300 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 40 does should be more than 55 kg. If the average weight is less than 55 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 40 does is less than 55 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 59.9 kg for 40 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 40 does in December, and the average weight was

x

= 59.9 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.    Since the sample average is below the mean, it is quite likely that the doe population is undernourished.Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 50.0 kg and standard deviation σ = 8.6 kg. Suppose a doe that weighs less than 41 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)

(b) If the park has about 2700 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.) does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 65 does should be more than 47 kg. If the average weight is less than 47 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 65 does is less than 47 kg (assuming a healthy population)? (Round your answer to four decimal places.)

(d) Compute the probability that x < 51.6 kg for 65 does (assume a healthy population). (Round your answer to four decimal places.)

Suppose park rangers captured, weighed, and released 65 does in December, and the average weight was x = 51.6 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 60.0 kg and standard deviation σ = 8.6 kg. Suppose a doe that weighs less than 51 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2900 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 65 does should be more than 57 kg. If the average weight is less than 57 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight x for a random sample of 65 does is less than 57 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that x< 61 kg for 65 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 65 does in December, and the average weight was x= 61 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite likely that the doe population is undernourished.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.    

Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 52.0 kg and standard deviation σ = 9.0 kg. Suppose a doe that weighs less than 43 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2100 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 70 does should be more than 49 kg. If the average weight is less than 49 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 70 does is less than 49 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 53.6 kg for 70 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 70 does in December, and the average weight was

x

= 53.6 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is above the mean, it is quite likely that the doe population is undernourished.    Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished.Since the sample average is below the mean, it is quite likely that the doe population is undernourished.

Let x be a random variable that represents the weights in kilograms (kg) of healthy adult female deer (does) in December in a national park. Then x has a distribution that is approximately normal with mean μ = 60.0 kg and standard deviation σ = 8.0 kg. Suppose a doe that weighs less than 51 kg is considered undernourished.

(a) What is the probability that a single doe captured (weighed and released) at random in December is undernourished? (Round your answer to four decimal places.)


(b) If the park has about 2500 does, what number do you expect to be undernourished in December? (Round your answer to the nearest whole number.)
does

(c) To estimate the health of the December doe population, park rangers use the rule that the average weight of n = 60 does should be more than 57 kg. If the average weight is less than 57 kg, it is thought that the entire population of does might be undernourished. What is the probability that the average weight

x

for a random sample of 60 does is less than 57 kg (assuming a healthy population)? (Round your answer to four decimal places.)


(d) Compute the probability that

x

< 61.2 kg for 60 does (assume a healthy population). (Round your answer to four decimal places.)


Suppose park rangers captured, weighed, and released 60 does in December, and the average weight was

x

= 61.2 kg. Do you think the doe population is undernourished or not? Explain.

Since the sample average is below the mean, it is quite likely that the doe population is undernourished. Since the sample average is above the mean, it is quite likely that the doe population is undernourished.     Since the sample average is below the mean, it is quite unlikely that the doe population is undernourished. Since the sample average is above the mean, it is quite unlikely that the doe population is undernourished.

Strassel Investors buys real estate, develops it, and resells it for a profit. A new property is available, and Bud Strassel, the president and owner of Strassel Investors, believes if he purchases and develops this property it can then be sold for $160,000. The current property owner has asked for bids and stated that the property will be sold for the highest bid in excess of $100,000. Two competitors will be submitting bids for the property. Strassel does not know what the competitors will bid, but he assumes for planning purposes that the amount bid by each competitor will be uniformly distributed between $100,000 and $150,000.

Develop a worksheet that can be used to simulate the bids made by the two competitors. Strassel is considering a bid of $130,000 for the property. Using a simulation of 1000 trials, what is the estimate of the probability Strassel will be able to obtain the property using a bid of $130,000? Round your answer to 1 decimal place. Enter your answer as a percent.

%

How much does Strassel need to bid to be assured of obtaining the property?

$  

What is the profit associated with this bid?

$  

Use the simulation model to compute the profit for each trial of the simulation run. With maximization of profit as Strassel’s objective, use simulation to evaluate Strassel’s bid alternatives of $130,000, $140,000, or $150,000. What is the recommended bid, and what is the expected profit?

A bid of results in the largest mean profit of $  .