The amount of time a bank teller spends with each customer is normally distributed with a mean of 3.10 minutes and a standard
deviation of 0.40 minutes. (Use the z table)
If a random sample of 16 customers is selected from the bank, what is the probability that the average time spent per customer will be at least 3 minutes?

There is an 85 percent chance that the sample mean will be below how many minutes?

Doubting Thomas does not believe that the mean is actually 3.10 minutes since he has often waited longer. He decides to conduct a study and generates a random sample of 25 customers. He calculates the waiting time for all 25 customers and finds the average A waiting time to be 4 minutes. Based on this information, what is the best estimate of the population mean assuming 95 percent accuracy. Is the doubting Thomas correct in his assumption?

Solution Summary

The solution provides step by step method for the calculation of Normal probabilities and t test for mean. Formula for the calculation and Interpretations of the results are also included. Interactive excel sheet is included. The user can edit the inputs and obtain the complete results for a new set of data.

A continuous random variable, x, is normally distributed with a mean of $1000 and a standard deviation of $100. Convert each of the following x values into its corresponding z-score.
a. x = $1000
b. x = $750
c. x = $1100
d. x = $950
e. x = $1225
2.Using the standard normal table, find the following probabilities

If x is normally distrubed with u = 20.0 and o = 4.0, determine the following:
a. P(x > 20.0)
b. P(16.0 < x < 24.0)
c. P(X < 12)
d. P(x = 22.0)
e. P(12.0 , x , 28.0)
f. P(x 15)

Standard normal probabilities
Let Z be a standard normal random variable. Calculate the following probabilities using the calculator provided. Round your responses to at least three decimal places.
P (z > - 0.82) =
P (z ≤ 0.77) =
P( -0.81 < z < 1.25) =

Find the indicated probabilities.
a. P (z > -0.89)
b. P (0.45 < z < 2.15)
Write the binomial probability as a normal probability using the continuity correction.
Binomial Probability Normal Probability
c. P ( x ≤ 56) P ( x < ? )
d. P ( x = 69 ) P ( ? < x < ?

A medical testfor malaria is subject to some error. Given a person who has malaria, the
probability that the test will fail to reveal the malaria is 0.06. Given a person who does not
have malaria, the test will correctly identify that the person does not have malaria with
probability 0.91. In a particular area, 20% of the

Statistics Practice Problems
SHOW ALL WORK
1. Given the following probabilities, Find Zo. Note: Graphs must be shown.
a) P(-2.67≤ z ≤ Zo) = 0.9718
b) P(Zo ≤ z ≤ 2.98) = 0.1117
2. Find the following probabilities: if µ = 160, σ = 16. Note: Graphs must be shown.
a) P(X > xo

Suppose x is a normally distributed random variable with y=13 and o=2. Find the following probabilities:
1. P (x is greater than or equal to 13.5)
2. P (13.44 is less or equal to x and 18.18 is greater than or equal to x).

Using the standard normal table, find the following probabilities associated with z:
a. P(0.00 ≤ z ≤ 1.25)
b. P(-1.25 ≤ z ≤ 0.00)
c. P(-1.25 ≤ z ≤ 1.25)
Using the standard normal table, find the following probabilities associated with z:
a. P (-0.36 ≤ z ≤ 0.00)
b. P(z ≤ -0.36)
c. P(z ≥ -0.43)