Determine the smallest sample size required to estimate the population mean under the given specifications in parts a through d below.

a. e=2.6​, confidence level=90​%, data between 70 and 150

The smallest sample size required to estimate the population mean is . ​(Round up to the nearest whole number as​ needed.)

STAT 150 The amount X, in GBs, of mobile data Sam uses in a given month is uniformly distributed between 0 and 10. The mobile data plan Sam is subscribed to charges Y dollars per months, where

Y = 20 X < 3，

=10 [X], 3 ≤ X < 6,

=10X X ≥ 6.

where [X] denotes the floor of x.

(1) What is the probability P (Y < 45)?

(2) What is the E(Y)?

A die is rolled 50 times and the following are the outputs:

6 1 3 4 2 6 3 5 1 3 6 1 6 6 3 3 6 5 2 4 1 6 5 3 1 2 5 2 1 2 4 1 4 1 5 5 6 6 2 1 1 2 5 6 5 5 6 3 1 3

What is the p-value of the chi-square test that the die is unbiased?

Computers Magazine has recently completed an analysis of its customer base. It has deter- mined that 75% of the issues sold each month are subscriptions and the other 25% are sold at newsstands. It has also determined that the ages of its subscribers are normally distributed with a mean of 44.5 and a standard deviation of 7.42 years, whereas the ages of its newsstand customers are normally distributed with a mean of 36.1 and a standard deviation of 8.20 years.

(a) Computers Magazine would like to make the following statement to its advertisers: “80% of our subscribers are between the ages of . . . and . . . .” Your job is to fill in the blanks, choosing a range that is symmetric around the mean. (In other words, the mean age of subscribers should be the midpoint of the range.) 1 plant manager of a manufacturing facility is concerned about drug use among plant

(b) What proportion of Computers Magazine newsstand customers have ages in the range you gave in (a)?

(c) What proportion of all of Computers Magazine customers have ages in the range you gave in (a)?

The American Heart Association is about to conduct an anti-smoking campaign and wants to know the fraction of Americans over 2222 who smoke.

Step 2 of 2 :  

Suppose a sample of 1421 Americans over 22 is drawn. Of these people, 953 don't smoke. Using the data, construct the 90% confidence interval for the population proportion of Americans over 22 who smoke. Round your answers to three decimal places.

Neighborhood Insurance sells fire insurance policies to local homeowners. The premium is $240, the probability of a fire is 0.1%, and in the event of a fire, the insured damages (the payout on the policy) will be $230,000.

a. Make a table of the two possible payouts on each policy with the probability of each.

b. Suppose you own the entire firm, and the company issues only one policy. What are the expected value, variance and standard deviation of your profit?

c. Now suppose your company issues two policies. The risk of fire is independent across the two policies. Make a table of the three possible payouts along with their associated probabilities. (Round your "Probability" answers to 4 decimal places.)

d. What are the expected value, variance and standard deviation of your profit?

e. Compare your answers to (b) and (d). Did risk pooling increase or decrease the variance of your profit?

f. Continue to assume the company has issued two policies, but now assume you take on a partner, so that you each own one-half of the firm. Make a table of your share of the possible payouts the company may have to make on the two policies, along with their associated probabilities. (Round your "Probability" answers to 4 decimal places.)

g. What are the expected value and variance of your profit?

Sales personnel for Skillings Distributors submit weekly reports listing the customer contacts made during the week. A sample of 67 weekly reports showed a sample mean of 19.5 customer contacts per week. The sample standard deviation was 5.2.

Provide a 90% confidence interval for the population mean number of weekly customer contacts for the sales personnel. (Round your answers to two decimal places.)

contacts/week to contacts/week

Provide 95% confidence interval for the population mean number of weekly customer contacts for the sales personnel. (Round your answers to two decimal places.)

contacts/week to contacts/week

A person must score within the top 2% of the population on an IQ test to qualify for membership in Mensa, the international high-IQ society. There are 110,000 Mensa members in 100 countries throughout the world (Mensa International website, January 8, 2013). Assume IQ scores are normally distributed with a mean of 100 and a standard deviation of 12.

a. What is the probability that a randomly selected person has an IQ less than 110?
b. What is the probability that a randomly selected person has an IQ higher than 133?
c. What is the probability that a randomly selected person has an IQ between 110 and 120?
d. What score must a person have to qualify for Mensa?

You have been tracking how much you spend on gas every month for several months and found that on average you spend about $60 per month. If you had to guess, what would you expect the IQR (Interquartile Range) of your gas spending to be? Would $1, $10 or $100 be most logical? Give statistical reasoning to back up your answer.

What is external validity? What is internal validity? Why do you need both?

Stock price today at $100. A binary PUT with strike of 85 is priced at $0.15. What is the implied standard deviation?

1. Let X be the uniform distribution on [-1, 1] and let Y be the uniform distribution on [-2,2].

a) what are the p.d.f.s of X and Y resp.?

b) compute the means of X, Y. Can you use symmetry?

c) compute the variance. Which variance is higher?

2. Starting salaries. You are planning a survey of starting salaries for recent computer science majors. In the latest survey by the National Association of Colleges and Employers, the average starting salary was reported to be $61,287. If you assume that the standard deviation is $3850, what sample size do you need to have a margin of error equal to $500 with 95% confidence? (report as an integer)

3. Suppose that in the setting of question 2 you have resources to contact 300 recent graduates. If all respond, what would be your margin of error? (report to nearest integer).

4. Suppose that in the setting of question 2 you have resources to contact 300 recent graduates. If only 50% respond, what would be your margin of error? (report to nearest integer).

A study group is to be selected from 5 freshmen, 7 sophomores, and 4 juniors. a. If a study group is to consist of 4 freshmen, 6 sophomores, and 2 juniors, how many different ways can the study group be selected? b. If a study group consisting of 6 students is selected, what is the probability that the group will consist of 2 freshmen, 3 sophomores, and 1 junior?