# Statistic homework help

Question

Which of the following data sets is most likely to be normally distributed? For other choices, explain why you believe they would not follow a normal distribution.

The hand span (measured from the tip of the thumb to the tip of the extended 5th finger) of a random sample of high school seniors.

The annual salaries of all employees of a large shipping company

The annual salaries of a random sample of 50 CEOs of major companies (25 men and 25 women)

The dates of 100 pennies taken from a cash drawer in a convenience store

Question

Assume than the mean weight of 1 year old girls in the US is normally distributed with a mean value of 9.5 kg and standard deviation of 1.1. Without using a calculator (use the empirical rule 68 %, 95 %, 99%), estimate the percentage of 1 year old girls in the US that meet the following conditions. Draw a sketch and shade the proper region for each problem…

Less than 8.1 kg

Between 7.3 and 11.7 kg.

More than 12.8 kg.

Question

The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.

65

83

93

100

Question

The grades on a marketing research course midterm are normally distributed with a mean (81) and standard deviation (6.3) . Calculate the z score for each of the following exam grades. Draw and label a sketch for each example.

65

83

93

100

Question…

What is the relative frequency of observations below 1.18? That is, find the relative frequency of the event Z < 1.18.

z .00 .01 … .08 .09

0.0 .5000 .5040 … .5319 .5359

0.1 .5398 .5438 … .5714 .5753

… … … … … …

1.0 .8413 .8438 … .8599 .8621

1.1 .8643 .8665 … .8810 8830

1.2 .8849 .8869 … .8997 .9015

… … … … … …

Question

Find the value z such that the event Z > z has relative frequency 0.80.

Question

For borrowers with good credits the mean debt for revolving and installment accounts is $ 15, 015. Assume the standard deviation is $3,540 and that debt amounts are normally distributed.

What is the probability that the debt for a borrower with good credit is more than $ 18,000.

Question

The average stock price for companies making up the S&P 500 is $30, and the standard deviation is $ 8.20. Assume the stock prices are normally distributed.

How high does a stock price have to be to put a company in the top 10 % … ?

Question

The scores on a statewide geometry exam were normally distributed with μ=72 and σ=8. What fraction of test-takers had a grade between 70 and 72 on the exam? Use the cumulative z-table provided below.

z. 00 .01 .02. 03. 04. 05. 06. 07 .08 .09

0.00. 50000 .50400 .50800 .51200 .51600 .51990 .52390 .52790 .53190 .5359

0.10. 53980 .54380 .54780 .55170 .55570 .55960 .56360 .56750 .57140 .5753

0.20. 57930 .58320 .58710 .59100 .59480 .59870 .60260 .60640 .61030 .6141

0.30. 61790 .62170 .62550 .62930 .63310 .63680 .64060 .64430 .64800 .6517

0.40. 65540 .65910 .66280 .66640 .67000 .67360 .67720 .68080 .68440 .6879

0.50. 69150 .69500 .69850 .70190 .70540 .70880 .71230 .71570 .71900 .7224

0.60. 72570 .72910 .73240 .73570 .73890 .74220 .74540 .74860 .75170 .7549

0.70. 75800 .76110 .76420 .76730 .77040 .77340 .77640 .77940 .78230 .7852

0.80. 78810 .79100 .79390 .79670 .79950 .80230 .80510 .80780 .81060 .8133

0.90. 81590 .81860 .82120 .82380 .82640 .82890 .83150 .83400 .83650 .8389

1.00. 84130 .84380 .84610 .84850 .85080 .85310 .85540 .85770 .85990 .8621

Question

The scores on a marketing research take home exam is normally distributed with μ=70.25 and σ=3.

Henry scored 71 on the exam Henry’s exam grade was higher than what percentage of test-takers?

Question

You sample 36 apples from your farm’s harvest of over 200,000 apples. The mean weight of the sample is 112 grams (with a 40 gram sample standard deviation). What is the probability that the weight of all 200,000 apples is within 100 and 124 grams?

Question

In a local teaching district a technology grant is available to teachers in order to install a cluster of four computers in their classrooms. From the 6250 teachers in the district, 250 were randomly selected and asked if they felt that computers were essential teaching tool for their classroom. Of those selected, 142 teachers felt that computers were an essential teaching tool.

Calculate a 99 % confidence interval for the proportion of teachers who felt that computers are an essential teaching tool.

How could the survey be changed to narrow the confidence interval but to maintain the 99 % confidence interval?

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