A European growth mutual fund specializes in stocks from the British Isles, continental Europe, and Scandinavia. The fund has over 250 stocks. Let x be a random variable that represents the monthly percentage return for this fund. Suppose x has mean μ = 1.4% and standard deviation σ = 1%.

(b) After 9 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)


(c) After 18 months, what is the probability that the average monthly percentage return x will be between 1% and 2%? (Round your answer to four decimal places.)

(e) If after 18 months the average monthly percentage return x is more than 2%, would that tend to shake your confidence in the statement that μ = 1.4%? If this happened, do you think the European stock market might be heating up? (Round your answer to four decimal places.)
P(x > 2%) =

7. The Supplemental Assistance Nutritional Program is the name for the federal government Food stamp program. At the end of the year 2014 the national statistics were staggering of 114 million households, 23 million were receiving food stamps. Social scientists wish to know if the percentage of California households receiving food stamps is the same as that of Florida. Random samples of 1,000 households are obtained for California and Florida and the number of households receiving food stamps is 180 and 150, respectively.

a. Find the percentage of households in the sample receiving food stamps for California and Florida.

b. Test the hypothesis that the "percentage of households receiving food stamps is the same in California as it is in Florida". Write the appropriate null and alternative hypotheses and use a significance level of 0.05. Make sure to give a decision and write a conclusion.

c. Compute the 95% Confidence Interval for the difference in the percentage of households receiving food stamps in California and Florida.

d. Does the Confidence Interval computed in part c agree with your decision in part b? Answer Yes or No and explain.

CASE STUDY: Chest Sizes of Scottish Militiamen (p. 306):

1. The population mean and population standard deviation of the chest circumferences are 39.85 and 2.07, respectively, identify the normal curve that should be used for the chest circumferences
2. Use the table above to find the percentage of militiamen in the survey with chest circumference between 36 and 41 inches, inclusive. Note: as the circumferences were rounded to the nearest inch, you are actually finding the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches
3. Use the normal curve you identified in part (a) to obtain an approximation to the percentage of militiamen in the survey with chest circumference between 35.5 and 41.5 inches. Compare your answer to the exact percentage found in part (b).

At one point the average price of regular unleaded gasoline was $3.53 per gallon. Assume that the standard deviation price per gallon is ​$0.07

per gallon and use​ Chebyshev's inequality to answer the following.

​(a) What percentage of gasoline stations had prices within 3 standard deviations of the​ mean?

​(b) What percentage of gasoline stations had prices within 2.5 standard deviations of the​ mean? What are the gasoline prices that are within 2.5 standard deviations of the​ mean?

​(c) What is the minimum percentage of gasoline stations that had prices between $3.39 and $3.67​?

​(a) At least _​__% of gasoline stations had prices within 3 standard deviations of the mean.(Round to two decimal places as​ needed.)

​(b) At least ___% of gasoline stations had prices within 2.5 standard deviations of the mean.​(Round to two decimal places as​ needed.)

The gasoline prices that are within 2.5 standard deviations of the mean are ​$_to ​$_.​(Use ascending​ order.)

​(c) _​__% is the minimum percentage of gasoline stations that had prices between $ 3.39 and $3.67.

6. Unanticipated changes in the rate of inflation

Initially, Neha earns a salary of $400 per year and Lorenzo earns a salary of $200 per year. Neha lends Lorenzo $100 for one year at an annual interest rate of 20% with the expectation that the rate of inflation will be 16% during the one-year life of the loan. At the end of the year, Lorenzo makes good on the loan by paying Neha $120. Consider how the loan repayment affects Neha and Lorenzo under the following scenarios.

Scenario 1: Suppose all prices and salaries rise by 16% (as expected) over the course of the year. In the following table, find Neha's and Lorenzo's new salaries after the 16% increase, and then calculate the $120 payment as a percentage of their new salaries. (Hint: Remember that Neha's salary is her income from work and that it does not include the loan payment from Lorenzo.)

Scenario 2: Consider an unanticipated decrease in the rate of inflation. The rise in prices and salaries turns out to be 5% over the course of the year rather than 16%. In the following table, find Neha's and Lorenzo's new salaries after the 5% increase, and then calculate the $120 payment as a percentage of their new salaries.

An unanticipated decrease in the rate of inflation benefits   and harms   .

An apple orchard farmer wants to know the true population proportion of all apples harvested at their farm which have the less valuable condition of being blemished, or in other words, are cider apples.

This true population proportion is a parameter value represented by the symbol p. As a population parameter, this value can never be known with certainty. It can however, be estimated with varying levels of confidence.

To estimate this parameter p, the farmer draws a simple random sample (SRS) of 524 apples from the orchard. Within this sample, the farmer finds that exactly 47 of the apples are cider apples.

The farmer then computes a 96%-level confidence interval estimate for the parameter p.

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Lower Limit of this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Upper Limit of this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

In percentage form, and rounded to four digits past the decimal point: What is the approximate value of the Margin of Error for this confidence interval?

Include a percentage symbol at the end of your numerical answer (with no spaces).

Suppose the farmer now wishes that they had instead built a confidence interval with a 99% confidence level, and a margin of error no greater than 2%.

To achieve these new specifications: The farmer intends to draw another SRS of apples in the future, and build another confidence interval.

What minimum sample size of apples will the farmer have to draw, in order to achieve these new confidence interval specifications?

(Note: Your answer should be a whole number here.)

A political pollster is conducting an analysis of sample results in order to make predictions on election night. Assuming a​ two-candidate election, if a specific candidate receives at least 54% of the vote in the​ sample, that candidate will be forecast as the winner of the election. You select a random sample of 100 voters. Complete parts​ (a) through​ (c) below.

a.

The probability is ______ that a candidate will be forecast as the winner when the population percentage of her vote is 50.1​%.

b.

The probability is _____that a candidate will be forecast as the winner when the population percentage of her vote is 56​%

c.