Homework 2 Due Friday, Jan. 29
1. Assume that the weight loss for the first month of a diet program varies between 6 pounds and 12 pounds, and is spread evenly over
the range of possibilities, so that there is a uniform distribution. Find the probability that a randomly selected person lost between 7
and 11 pounds.
2. A survey among freshmen at a certain university revealed that the number of hours spent studying the week before final exams was
approximately normally distributed with mean 25 and standard deviation 7.
a. What proportion of students studied more than 20 hours?
b. What proportion of students studied less than 16 hours?
c. What proportion of the students studied between 25 and 40 hours?
3. In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the
United States are approximately normally distributed with mean 80.5 and standard deviation 9.9.
a. Find the probability that a randomly selected adult woman will have a diastolic blood pressure greater than 85?
b. Find the 40th percentile of the blood pressures.
c. A random sample of size 81will be drawn from the population. What is the probability that the sample mean will be greater than
78.5?
4. The IQs of all college freshmen last year were approximately normally distributed, with a mean of 115 and a standard deviation of
8. The middle 50% of the IQs are between what two IQs?
5. Cucumbers grown on a certain farm have weights that are normally distributed with a standard deviation of 2 ounces. What is the
mean weight if 85% of the cucumbers weigh less than 16 ounces?
6. A math teacher gives two different tests to measure students' aptitude for math. Scores on the first test are normally distributed with
a mean of 23 and a standard deviation of 4. Scores on the second test are normally distributed with a mean of 64 and a standard
deviation of 10. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test,
what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)
7. Suppose the amount of a popular sport drink in bottles leaving the filling machine has approximately a normal distribution with
mean 101.5 milliliters (ml) and standard deviation 1.6 ml.
a. If the bottles are labeled 100 ml, what proportion of the bottles contain less than the labeled amount?
b. If only 2.5% of the bottles have contents that exceed a specified amount c, what is the value of c?
8. For a standard normal distribution, find the percentage of data that are more than 2 standard deviations below the mean or more
than 3 standard deviations above the mean.
9. Consider the variable x = time required for a college student to complete a standardized exam. Suppose that for the population of
students at a particular university, the distribution of x is well approximated by a normal curve with mean 45 min and standard
deviation 5 min. Consider random samples of size 25 from the population.
a. Sketch the sampling distribution of the sample mean. You need not get the graph perfectly correct, but should clearly indicate
different aspects of the distribution, such as mean, standard deviation, and shape.
Mean (  x ) =
Standard deviation (  x ) =
Shape:
Sketch the sampling distribution of the sample mean.
b. What is the probability that a sample of size n=25 from the population would result in a sample mean greater than 46 minutes?
c. Find k such that
P( x  k )  .10