# Normal Probability Using the Z Score

1) The average amount of participation in Dallas, Texas, during the month of April is 3.5 inches Assume that a normal distribution applies and that the standard deviation is .8 inches.

What percentage of the time dose the amount of rainfall in April exceed 5 inches?

What percentage of the time is the amount of rainfall in April less than 3 inches?

A month is classified as extremely wet if the amount of rainfall is in the upper 10% for that month. How much precipitation must fall in April for it to be classified as extremely wet?

2) Trading volume of the New York Stock exchange is heaviest during the first half hour early morning, and last half hour late afternoon, of the trading day. The early morning trading volumes Millions of shares for 13 days in January and February are shown here January 23, 2006, February 27, 2006.

214 163 265 194 180

202 198 212 201

174 171 211 211

Compute the mean and standard deviation to use as estimates of the population mean and standard deviation.

What is the probability that on a randomly selected day the early morning trading volume will be less than 180 million shares?

What is the probability that ,on a randomly selected day the early morning trading volume will exceed 230 million shares?

How many shares would have to be traded for the early morning trading volume on a particular day to be among the busiest 5% of days?

3) The U.S. Bureau of Labor statistics reports that the average annual expenditure on food and drink for all families is $5700 Assume that annual expenditure of food and drink is normally distributed and that the standard deviation is $1500.

What is the range of expenditures of 10% of families with the lowest annual spending on food and drink?

What percentage of families spend more than $7000 annually on food and drink?

What is the range of expenditures for 5% of families with the highest annual pending on food and drink?

4) Suppose a single random sample of six 50 is selected from a population with σ=10 find the value of the standard error of the mean in each of the following cases use the finite population correction factor if appropriate:

The population size is infinite

The population size is N= 50,000

The population size is N=5000

The population size is N=500

5) The College Board American college testing program reported a population mean SAT score of µ=1020 Assume that the population standard deviation is σ= 100.

What is the probability that a random sample of 75 students will provide a sample mean Sat score with 10 of the population mean?

What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean?

6) A population process is checked periodically by a quality control inspector. The inspector selects simple random samples of 30 finished products and computes the sample mean product weights. If test results over a long period of time show that 5% of the x values are over 2.1 pounds and 5% are under 1.9 pounds, what are the mean and the standard deviation for the population of products produced with this process?

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#### Solution Summary

The solution provides step by step method for the calculation of probability using the Z score. Formula for the calculation and Interpretations of the results are also included.

Normal Probabilities - Using Z Score

A normal distribution has a mean of u= 40 and o=10. if a vertical line is drawn through the distribution at x= 55, what proportion of the scores on the right side of the line?

A normal distribution has a u= 80 and o= 10. what is the probability of randomly selecting a score greater than 90 from this distribution?

A normal distribution has a mean of u= 100 and o= 20. if one score is randomly selected from the probability that the score will be less than x= 84?

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