Assume that the heights of women are normally distributed with a mean of 63.6 inches and a
standard deviation of 2.5 inches. If 100 women are randomly selected, find the probability
that they have a mean height greater than 63.0 inches?
Assume that the salaries of elementary school teachers in the United States are normally
distributed with a mean of $32,000 and a standard deviation of $3000. If 100 teachers are
randomly selected, find the probability that their mean salary is greater than $32,500?
Choose the correct Answer.
A study performed on some type of batteries indicates that the average life time of the
battery is 2.4 months, and the standard deviation is 0.9. If a battery is selected at random,
find the probability that the battery’s life will be less than 3.4 months. Assume the
variables for battery is normally distributed?
You are taking a multiple choice test for which you have mastered 70% of the material.
Assume this means that you have a 0.7 chance of knowing the answer to a random test
question, and that if you don’t know the answer to a question then you randomly select
among the four answer choices. Finally, assume that this holds for each question, independent of the others.
(a) What is your expected score (as a percent) on the exam?
Let p be the probability of getting a random question correct. You likely found p in part
(a), but in any case you should assume 0.7 < p < 0.9.
In parts (b), (c) and (d) you can just use the letter p for this probability.
(b) If the test has 10 questions, what is the probability you score 90% or higher? (Do not
simplify the expression you get.)
(c) What is the probability you get the first 6 questions on the exam correct? (Again, do
not simplify the expression you get.)
(d) Suppose you need a 90% to keep your scholarship. Would you rather have a test with
10 or 100 questions? Why? (Your answer only needs to be one sentence long.)
