# Normal Distribution, Finding Probability, Sample size

Question (1)

The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share.

a. What percent of the days was the price over $45.00? How many days

would you estimate?

b. What percent of the days was the price between $38.00 and $40.00?

c. What was the stock's price on the highest 15 percent of days?

Question (2):

You are to conduct a sample survey to determine the mean family income in a rural area of central Florida. The question is, how many families should be sampled? In a pilot sample of 10 families, the standard deviation of the sample was $500. The sponsor of the survey wants you to use the 95 percent confidence level. The estimate is to be within $100. How many families should be interviewed?

Question (3):

The mean SAT score for Division I student-athletes is 947 with a standard deviation of 205. If you select a random sample of 60 of these students, what is the probability the mean is below 900?

For full description of the questions, please see the attached questions file.

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#### Solution Preview

Solution (1)

the required percentage = 0.0918 × 100 = 9.18 %

No. of days estimated = 22 days

percent of days during which the price was between $38 and $40 = 14.92%

stocks price on ...

#### Solution Summary

The solutions to above described problems are given in detailed step by step manner so that the students could use these solutions to solve other problems of the same type without any difficulty at their own efforts. The problems deal with finding required probability, Finding percent of population, finding sample size with 95% confidence level, and using Margin of erro.

The solutions are explained in such a way that the students will not have any difficulty in understanding how to work out similar problems.