# Standard Deviation

The College Board American College Testing Program reported a population mean SAT score of  =1017. Assume that the population standard deviation is  = 100.

a. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

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

31

Business Week reports that its subscribers who plan to purchase a new vehicle plan to spend a mean of $27, 100. Assume that the new vehicle price for the population of Business Week subscribers has a mean of  = $27,100 and a standard deviation of  = $5,200.

a. What is the probability that the sample mean new vehicle price for a sample of 30 subscribers is within $1,000. of the population mean?

b. What is the probability that the sample mean new vehicle price for a sample of 50 subscribers is within $1,000 of the population mean?

19.

The average amount of precipitation in Dallas, Texas, during the month of Aprils is 3.5 inches. Assume that the normal distribution applies and that the standard deviation is .8 inches.

a. What percentage of the time does the amount of rainfall in April exceed 5 inches?

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

23.

The time needed to complete the final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?

#### Solution Preview

27. The College Board American College Testing Program reported a population mean SAT score of m =1017. Assume that the population standard deviation is s = 100.

<br>

<br>a. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

<br>

<br>Find the probability of within D=+-5 of the mean.

<br>The standard error is SE= s/SQRT(N) = 100/SQRT(75)= 11.547

<br>Then calculate z value by formula: z = D/SE= 5/11.547 = 0.433

<br>Prob(D<5)=Prob(Z<0.433) = 0.667 from a z-table

<br>So Prob (D<-5)= Prob(Z<-0.433) =Prob(Z>0.433) = 1-0.667=0.333

<br>So Prob (-5<D<5)=Prob(Z<0.433) - Prob(Z<-0.433) = 0.667-0.333=0.334

<br>

<br>b. What is the probability a random sample of 75 students will provide a sample mean SAT score within 20 of the population mean?

<br>

<br>Find the probability of within D=+-10 of the mean.

<br>The standard error is SE= s/SQRT(N) = 100/SQRT(75)= 11.547

<br>Then calculate z value by formula: z = D/SE= 10/11.547 = ...

#### Solution Summary

27.

The College Board American College Testing Program reported a population mean SAT score of  =1017. Assume that the population standard deviation is  = 100.

a. What is the probability that a random sample of 75 students will provide a sample mean SAT score within 10 of the population mean?

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

31

Business Week reports that its subscribers who plan to purchase a new vehicle plan to spend a mean of $27, 100. Assume that the new vehicle price for the population of Business Week subscribers has a mean of  = $27,100 and a standard deviation of  = $5,200.

a. What is the probability that the sample mean new vehicle price for a sample of 30 subscribers is within $1,000. of the population mean?

b. What is the probability that the sample mean new vehicle price for a sample of 50 subscribers is within $1,000 of the population mean?

19.

The average amount of precipitation in Dallas, Texas, during the month of Aprils is 3.5 inches. Assume that the normal distribution applies and that the standard deviation is .8 inches.

a. What percentage of the time does the amount of rainfall in April exceed 5 inches?

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

23.

The time needed to complete the final examination in a particular college course is normally distributed with a mean of 80 minutes and a standard deviation of 10 minutes.

a. What is the probability of completing the exam in one hour or less?

b. What is the probability that a student will complete the exam in more than 60 minutes but less than 75 minutes?