Reference no: EM132409377

1. Given that z is a Standard Normal random variable, find the following probabilities:

a. P(z<0.67)

b. P(z> -0.22)

c. P(-0.32<z<1.645)

2. Given that z is a Standard Normal random variable, find z for each situation:

a. the area to the left of z is 0.68

b. the area to the right of z is 0.68

c. the total area to the left of -z and to the right of z is 0.32

3. Given that x is a Normal random variable with a mean of 10 and standard deviation of 4, find the following probabilities:

a. P(x<6.7)

b. P(x>12.5)

c. P(8.8<x<12.5)

4. A simple random sample of 50 customers is selected from an account receivable portfolio and the sample mean account balance is $1000. The population standard deviation σ is known to be $200.

a. Construct a 95% confidence interval for the mean account balance of the population.

b. What is the margin of error for estimating the mean account balance at the 95% confidence level?

c. Construct a 95% confidence interval for the mean account balance of the population if the sample mean account balance is obtained from a random sample of 100 instead of 50.

d. Based on the results from a. and c., what can you say about the effect of a larger sample size on the length of the confidence interval at the same confidence level?