Download Practice problems 8- answers, Normal Distributions

Statistics and the TI-84
Practice Problems 8: normal distributions
1. A survey of salaries paid to graduates showed that the mean salary for public accounting
managers with six to nine years of experience was $47,000 Assume salaries are normally
distributed with a standard deviation of $5500.
a) What is the probability that a manager earns between $40,000 and $50,000?
 2nd DISTR 2 normalcdf(40000, 50000, 47000, 5500) ENTER
answer: 0.6057220789
b) What is the probability that a manager earns less than $35,000?
 2nd DISTR 2 normalcdf(-EE5, 35000, 47000, 5500) ENTER
answer: 0.014561425
c) How much do the top 1% of the public accounting managers with six to nine years of
experience earn?
 2nd DISTR 3 invnorm(0.99, 47000, 5500) ENTER
answer: 59794.91
2. The attendance at games at a certain stadium is normally distributed, with a mean of 45,000
and a standard deviation of 3,000.
For 80% of the time the attendance should be at least how many?
 2nd DISTR 3 invnorm(0.20, 45000, 3000) ENTER
answer: 42476
3. A survey asked working women what worries them most. Concern about low wages, job
stress, and health benefits were mentioned most of often, with 60% of working women
concerned about low wages .Consider a random sample of 500 working women from this
population.
a) What is the expected number of women in this group who will express a concern about low
wages?
answer :   np  500(0.60)  300
b) What is the standard deviation of the number who will express a concern about low wages?
answer :   npq  500(0.60)0.40  10.95445
c) What is the probability that 325 or more women will express a concern about low wages? Use
the normal approximation to the binomial with the  0.5 continuity correction factor.
 2nd DISTR 2 normalcdf(324.5, EE5, 300, 10.95445) ENTER
answer: 0.0126583641
d) What is the 40th percentile of the number of women who will express a concern about low
wages?
 2nd DISTR 3 invnorm(0.40, 300, 10.95445) ENTER
answer: 297
-76-
Exercise 4. Consider the distribution of sample means that results when samples of size n=36 are
taken from a population with mean   28 and standard deviation   12.
Using the central limit theorem,
a) find the probability that the mean of a sample is greater than 30.5.
 2nd DISTR 2 normalcdf(30.5, EE9, 28, 2) ENTER answer: 0.105649839
b) find the probability that a sample mean is between 25 and 27.
 2nd DISTR 2 normalcdf(25, 27, 28, 2) ENTER answer: 0.2417303035
c) find the 90th percentile of the distribution of sample means.
 2nd DISTR 3 invNorm(.90, 28, 2) ENTER answer: 30.56310313
Exercise 5. A Sociologist claims that the average amount of time adults spend watching
television is at least 12 hours a week with a standard deviation of 2 hours. To test his
claim a students takes a sample of 64 adults and asks then about the amount of time they
spend watching television. If the average of the sample is 11.5 or less, then he rejects the
Sociologist’s claim. If the Sociologist is correct, what is the probability that the student
will reject his claim?
 2nd DISTR 2 normalcdf(0, 11.5, 12, .25) ENTER answer: 0.022750062
Exercise 6. In problem 5, what is the probability that the student will reject the
Sociologist claim if the true average watching time is 11 hours (not 12).
 2nd DISTR 2 normalcdf(0, 11.5, 11, .25) ENTER answer: 0.977249938
-77-