67. Suppose that P(B) = 0.4, P(A|B) = 0.1 and P(A|B^c) = 0.9

(a) Calculate P(A)

(b) Calculate P(A|B)

71. Suppose a couple decides to have three children. Assume that the sex of each child is independent, and the probability of a girl is 0.48, the approximate figure in the US.

(a) How many basic outcomes are there for this experiment? Are they equally likely?

(b) What is the probability that the couple has at least one girl?

104. A multiple-choice quiz has 12 questions, each of which has 5 choices. To pass you need to get at least 8 of them correct. Nina forgot to study, so she simply guesses at random.

1. Let the random variable X denote the number of questions that Nina gets correct on the quiz. What kind of random variable is X? Specify all parameter values.

2. Calculate the probability that Nina passes the quiz.

According to Nielsen Media Research, the average number of hours of TV viewing by adults (18 and over) per week in the United States is 36.07 hours. Suppose the standard deviation is 8.8 hours and a random sample of 48 adults is taken.

a. What is the probability that the sample average is more than 35 hours?

b. What is the probability that the sample average is less than 36.6 hours?

c. What is the probability that the sample average is less than 28 hours? If the sample average actually is less than 40 hours, what would it mean in terms of the Nielsen Media Research figures?

d. Suppose the population standard deviation is unknown. If 75% of all sample means are greater than 34 hours and the population mean is still 36.07 hours, what is the value of the population standard deviation? (Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

The salinity, or salt content, in the ocean is expressed in parts per thousand (ppt). The number varies with depth, rainfall, evaporation, river runoff, and ice formation. The mean salinity of the oceans is 35 ppt. Suppose the distribution of salinity is normal and the standard deviation is 0.51 ppt, and suppose a random sample of ocean water from a region in a specific ocean is obtained.

What is the probability that the salinity is more than 36 ppt? (Round your answer to four decimal places.)

_____________

What is the probability that the salinity is less than 33.5 ppt? (Round your answer to four decimal places.)

____________

A certain species of fish can only survive if the salinity is between 33 and 35 ppt. What is the probability that this species can survive in a randomly selected area? (Round your answer to four decimal places.)

____________

Find a symmetric interval about the mean salinity such that 50% of all salinity levels lie in this interval. (Round your answers to four decimal places.)

_________ , __________

Parts are inspected on a production line for a defect. It is known that 5% of the pieces have this defect. (this applies to 5 parts of the problem)

to. If an inspector examines 12 parts, what is the probability of finding more than 2 defective parts? (10 pts)

b. What is the expected number of defective parts in 12-piece sample? (10 pts)

c. In another area, parts are inspected until 5 defective parts are found, then the machine is stopped to reset the machine. On average, how many pieces does the machine stop? (10 pts)

d. In another area, parts are inspected until 3 faulty parts are found, then the machine is stopped to reset the machine. What is the probability of needing between 55 and 60 pieces to stop the machine? (10 pts)

and. 100 pieces were separated for special tests. A sample of 15 pieces will be taken from these 100. What is the probability of finding at least 2 defects in the sample? (15 points)

There are 20 total socks, 10 white and 10 black. This makes 10 total matching pairs of 5 pair of white and 5 pair of black.

6. What is the total probability of picking a white sock and then another white sock (one pair of white socks)?

7. What is the probability of picking either a pair of white socks or a pair of black socks?

8. If each time you pick a sock from the drawer a sock just like it magically replaces it, what is the probability of picking either a pair of white socks or a pair of black socks?

9. How can you guarantee success of picking a matching pair? In other words, what is the minimum number of socks needing to be picked to guarantee a matching pair? (Hint: There is a right answer to this question!)

10. Explain dependent and independent trials and then further describe the difference between Question 7 and Question 8 as it relates to dependent and independent trials.

A person with a cough is a persona non grata on airplanes, elevators, or at the theater. In theaters especially, the irritation level rises with each muffled explosion. According to Dr. Brian Carlin, a Pittsburgh pulmonologist, in any large audience you'll hear about 18 coughs per minute.

(a) Let r = number of coughs in a given time interval. Explain why the Poisson distribution would be a good choice for the probability distribution of r. Coughs are a common occurrence. It is reasonable to assume the events are independent. Coughs are a common occurrence. It is reasonable to assume the events are dependent. Coughs are a rare occurrence. It is reasonable to assume the events are independent. Coughs are a rare occurrence. It is reasonable to assume the events are dependent.

(b) Find the probability of seven or fewer coughs (in a large auditorium) in a 1-minute period. (Use 4 decimal places.)

(c) Find the probability of at least eight coughs (in a large auditorium) in a 28-second period. (Use 4 decimal places.)

Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these Xi's have a multinomial distribution. Suppose it is claimed that the color proportions are p1 = 0.22, p2 = 0.13, p3 = 0.18, p4 = 0.2, p5 = 0.13, and p6 = 0.14. (a) If n = 12, what is the probability that there are exactly two M&Ms of each color? (Round your answer to four decimal places.) Correct: Your answer is correct. (b) For n = 20, what is the probability that there at most eight orange candies? [Hint: Think of an orange candy as a success and any other color as a failure.] (Round your answer to three decimal places.) (c) In a sample of 20 M&Ms, what is the probability that the number of candies that are blue, green, or orange is at least 8? (Round your answer to three decimal places.)

Ask Your Teacher

The local bakery bakes more than a thousand 1-pound loaves of bread daily, and the weights of these loaves varies. The mean weight is 2 lb. and 3 oz., or 992 grams. Assume the standard deviation of the weights is 30 grams and a sample of 35 loaves is to be randomly selected.

(b) Find the mean of this sampling distribution. (Give your answer correct to nearest whole number.)
grams

(c) Find the standard error of this sampling distribution. (Give your answer correct to two decimal places.)


(d) What is the probability that this sample mean will be between 988 and 996? (Give your answer correct to four decimal places.)


(e) What is the probability that the sample mean will have a value less than 986? (Give your answer correct to four decimal places.)


(f) What is the probability that the sample mean will be within 2 grams of the mean? (Give your answer correct to four decimal places.)

Customers arrive at a local grocery store at an average rate of 2 per minute.

(a) What is the chance that no customer will arrive at the store during a given two minute period?

(b) Since it is a “Double Coupon” day at the store, approximately 70% of the customers coming to the store carry coupons. What is the probability that during a given two-minute period there are exactly four (4) customers with coupons and one (1) without coupons?

(c) Divide one given hour into 30 two-minute periods. Suppose that the numbers of customers arriving at the store during those periods are independent of each other. Denote by X the number of the periods during which exactly 5 customers arrive at the store and 4 of them carry coupons. What is the probability that X is at least 2?

(d) What is the probability that exact 4 customers coming to the store during a given two-minute period carry coupons?

Part a

The Bogue High School Gift Shop purchases sweatshirts emblazoned with the school name and logo from a vendor in Montego Bay at a cost of $2,000 each. The annual holding cost for a sweatshirt is calculated as 1.5% of the purchase cost. It costs the Gift Shop $500 to place a single order. The Gift Shop manager estimates that 900 sweatshirts will be sold during each month of the upcoming academic year.

i) Determine the highest number of shirts that should be purchased by the Gift Shop in order to minimize stock administration costs.

ii) What is the number of orders to be placed each year?

iii)Compute the average annual ordering cost

iv) Compute the average annual carrying cost

v) Compute the total stock administration cost

Part b The maximum sale for the Gift Shop for any one week is 300 sweatshirts and minimum sales 150 sweatshirts. The vendor takes anywhere from 2 to 4 weeks to deliver the merchandise after the order is placed. Using the EOQ policy, determine the re-order level, minimum inventory level and maximum inventory level for the business