Question

2)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 132000 dollars. Assume the standard deviation is 31000 dollars. Suppose you take a simple random sample of 59 graduates.

Find the probability that a single randomly selected salary has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < X < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=59n=59 has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < ¯xx¯ < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

3)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.1 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.1 weeks and that the population standard deviation is 5.4 weeks. Suppose you would like to select a random sample of 91 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35 and 37.2.
P(35 < X < 37.2) =

Find the probability that a sample of size n=91n=91 is randomly selected with a mean between 35 and 37.2.
P(35 < ¯xx¯ < 37.2) =

Enter your answers as numbers accurate to 4 decimal places.

4)CNNBC recently reported that the mean annual cost of auto insurance is 957 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 73 auto insurance policies. (Do not use tables unless directed to do so.)

Find the probability that a single randomly selected value is more than 994 dollars.
P(X > 994) =

Find the probability that a sample of size n=73n=73 is randomly selected with a mean that is more than 994 dollars.
P(¯xx¯ > 994) =

Enter your answers as numbers accurate to 4 decimal places.

5)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 168000 dollars. Assume the standard deviation is 43000 dollars. Suppose you take a simple random sample of 70 graduates.

Do not use probability tables to find the probabilities below as they may not be accurate enough.

Find the probability that a single randomly selected salary is more than 164000 dollars.
P(X > 164000) =

Find the probability that a sample of size n=70n=70 is randomly selected with a mean that is more than 164000 dollars.
P(¯xx¯ > 164000) =

Enter your answers as numbers accurate to 4 decimal places.

6)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 9 weeks. Suppose you would like to select a random sample of 38 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 24.
P(X < 24) =

Find the probability that a sample of size n=38n=38 is randomly selected with a mean less than 24.
P(¯xx¯ < 24) =

Enter your answers as numbers accurate to 4 decimal places.

7)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 261.5-cm and a standard deviation of 0.5-cm. For shipment, 13 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 261.7-cm.
P(¯xx¯ < 261.7-cm) =

Enter your answer as a number accurate to 4 decimal places.

Answer 1