A magazine published data on the best small firms in a certain year. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. The table below shows the ages of the chief executive officers for the first 68 ranked firms.

(a) What is the frequency for CEO ages between (but not including) 54 and 65? (Enter your answer as a whole number.)


(b) What percentage of CEOs are 65 years or older? (Round your answer to the nearest whole number.)
%

(c) What is the relative frequency of ages under 50? (Round your answer to two decimal places.)


(d) What is the cumulative relative frequency for CEOs younger than 55? (Round your answer to two decimal places.)

Roller coaster ride: A roller coaster is being designed that will accommodate 60 riders. The maximum weight the
coaster can hold safely is 12,000 pounds. According to the National Health Statistics Reports, the weights of adult U.S.
men have mean 191 pounds and standard deviation 65 pounds, and the weights of adult U.S. women have mean 167 pounds and
standard deviation 74 pounds. Use the TI-84 Plus calculator.

Part 1 of 3

(a) If 60 people are riding the coaster, and their total weight is 12,000 pounds, what is their average weight?
The average weight is____ pounds.

Part 2 of 3
(b) If a random sample of 60 adult men ride the coaster, what is the probability that the maximum safe weight
will be exceeded? Round the answer to at least four decimal places.
If a random sample 60 adult men ride the coaster, the probability that the maximum safe weight will be exceeded is?

Part 3 of 3
(c) If a random sample of 60 adult women ride the coaster, what is the probability that the maximum safe weight will
be exceeded? Round the answer to at least four decimal places.
If a random sample 60adult women ride the coaster, the probability that the maximum safe weight will be exceeded is?

The population of weights of a particular fruit is normally distributed, with a mean of 727 grams and a standard deviation of 20 grams. If 2 fruits are picked at random, then 18% of the time, their mean weight will be greater than how many grams? Round your answer to the nearest gram.

Two random samples are taken, one from among UVA students and the other from among UNC students. Both groups are asked if academics are their top priority. A summary of the sample sizes and proportions of each group answering yes'' are given below:

UVA (Pop. 1):UNC (Pop. 2):n1=85,n2=100,p̂ 1=0.733p̂ 2=0.635UVA (Pop. 1):n1=85,p^1=0.733UNC (Pop. 2):n2=100,p^2=0.635

Find a 95.4% confidence interval for the difference p1−p2p1−p2 of the population proportions.

The firearms manufacturer that sells its firearms to the local sheriff’s department has 2000 used firearms to sell. Each used firearm has a 13% probability of needing major mechanical repairs. You randomly select 600 firearms for potential purchase.

What is the likelihood that 39 firearms will need major mechanical repairs? [Show your work]

What is the likelihood that all the firearms will work? [Show your work]

What is the likelihood that all the firearms will need major mechanical repairs? [Show your work]

1. Consider these situations. Which ones do you think the trend will be linear? Explain.

a) We measure the height (x) and armspan (y) of a number of UCLA students.
b) We collect data on the size houses (x) and their value (y) in a city.
c) For "industrialized" countries, we examine the relationship between their annual wine consumptions (liters per person) and mortality rate (deaths per 100,000).
d) For one year, a person uses a fitbit activity tracker to record the number of steps taken per day (x) and compares this to the number of steps recorded by his smartphone's activity tracker (y).

A population of values has a normal distribution with μ=77.7μ=77.7 and σ=35.8σ=35.8. A random sample of size n=240n=240 is drawn.

1. Find the probability that a single randomly selected value is between 74.2 and 82.6. Round your answer to four decimal places.
   P(74.2<X<82.6)=P(74.2<X<82.6)=
   
2. Find the probability that a sample of size n=240n=240 is randomly selected with a mean between 74.2 and 82.6. Round your answer to four decimal places.
   P(74.2<M<82.6)=P(74.2<M<82.6)=  

According to statistics reported on news source, a surprising number of motor vehicles are not covered by insurance. Sample results, consistent with the news report, showed 34 of 200 vehicles were not covered by insurance.

A. What is the point estimate of the proportion of vehicles not covered by insurance?

B. Develop a 95% confidence interval for the population proportion. (Round your answer to four decimal places.)

A school counselor has been working with a group of six-graders with special needs. She hypothesized that students like her group may have higher depression scores compared to the national average for six-graders. So she assessed her group of students with a depression scale for children and compared the scores to the national average through a t test. The t statistic turned out to be .20. Using a significance level of .01, what decision should she make regarding the null hypothesis?

A.Postpone any decisions until a more conclusive study could be conducted

B.There is not enough information given to make a decision

C.Reject it

D.Fail to reject it

Suppose x has a distribution with μ = 16 and σ = 10.

(a) If a random sample of size n = 45 is drawn, find μx, σ x and P(16 ≤ x ≤ 18). (Round σx to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(16 ≤ x ≤ 18) =

(b) If a random sample of size n = 72 is drawn, find μx, σ x and P(16 ≤ x ≤ 18). (Round σ x to two decimal places and the probability to four decimal places.)

μx =

σ x =

P(16 ≤ x ≤ 18) =

1. Consider the following production function for bus transportation in a particular city:

Q= a

Where Fuel input in gallons = F

Capital input in number of busses = K

Labor input in worker hours = L

Output in millions of bus miles = Q

We estimate the various parameters as follows using historical data:

                                    α=0.0012, β1=0.45, β2=0.2, β3=0.3

a) Determine output elasticities for Labor.

b) Suppose that labor hours increase by 10%. By what percentage will output increase?

The probability that a male will be​ color-blind is 0.046. Find the probabilities that in a group of 53 ​men, the following will be true. a. Exactly 5 are​ color-blind. b. No more than 5 are​ color-blind. c. At least 1 is​ color-blind.

Sports Score Hot Line Calls (Optional) Sports Scores Hot Line receives, on the average, 11 calls per hour requesting the latest sports scores. The distribution is Poisson in nature. For any randomly selected hour, find the probability that the company will receive

a. At least 7 calls

b. 4 or more calls

c. At most 9 calls