Download Chapter 6 1. It is reported that 70% of high school females engaged

Chapter 6
1. It is reported that 70% of high school females engaged in aerobics or dancing for
vigorous physical activity. A random sample of 8 students is taken this year.
(a) Find the probability that the sample contains 3 females who engaged in aerobics or
dancing.
(b) Repeat part(a) using binomial formula (not the table)
(c) Find the probability that the sample contains at most 2 females who engaged in
aerobics or dancing.
(d) Find the probability that the sample contains at least 5 females who engaged in
aerobics or dancing.
(e) What is the most likely number of females in the sample who engaged in aerobic or
dancing?
(f) If you find 2 out of the 8 students engaged in aerobic or dancing, would that be
considered as unusual?
2. It is reported that 55% of high school females engaged in aerobics or dancing for
vigorous physical activity. A random sample of 12 students is taken this year.
(a) Find the probability that the sample contains 6 females who engaged in aerobics or
dancing.
(b) Find the probability that the sample contains at most 3 females who engaged in
aerobics or dancing.
(c) Find the probability that the sample contains at least 11 females who engaged in
aerobics or dancing.
(d) What is the most likely number of females in the sample who engaged in aerobic or
dancing?
(e) If you find 11 out of the 12 students engaged in aerobic or dancing, would that be
considered as unusual?
3. Participants from the National Health and Nutrition Examination Survey, 2003–2004, had
a mean BMI(Body Mass Index) of 28.3 with a standard deviation of 6.0. Assume BMI is
normally distributed.
(a) What is the probability that a randomly selected participant had a BMI measure
between 25 and 32?
(b) What is the probability that a randomly selected participant had a BMI measure
below 28.3?
(c) Bottom 25% would be eligible for a food allowance from the government. What is
the cutoff BMI value to be eligible for the allowance?
4. Find the indicated probability for the standard normal distribution
(a) P(Z  2.87)
(b) P(1.64  Z  1.99)
(a) Find the Z value with an area of 0.1131 under the standard normal curve to
its right.
(b) Find the Z value with an area of 0.9082 under the standard normal curve to
its left.
(c) Find the Z value with an area of 0.9881 under the standard normal curve to
its left.
6 . The distribution of heights (X) of American women aged 18 to 24 is normally distributed
with mean 65.5 inches and standard deviation 2.5 inches.
(a) What is the probability that a randomly selected woman is between 60 and 64 inches
tall?
(b)Tallest 25% will be edible to be selected to the “basketball-pool”. What is the cutoff
to be selected to the “basketball-pool”?
7. (a) Find the Z-value with an area of 0.8051 under the standard normal curve to its right.
(b) Evaluate P(Z > -1.54).
©Find the 27th percentile of the Z distribution.
8 . Find the indicated probability for the standard normal
(a) P(Z > 1.67)
(b) P(-1.75< Z < 1.96)
© P(Z < -2.95)
(d) Find the 80th percentile of the Z distribution.
€ Find the Z-value with an area of 0.9357 under the standard normal curve to its right.
9.Find the mean and the standard deviation of the following distribution.
x
P(x)
0
.4
1
.1
3
.2
4
.3
10. Chipper Jones was the Major League Baseball league leader in 2008 according to batting
average. For the 2008 season, the percentage of Jones’ hits that resulted in 1, 2, 3, or 4
(home run) bases was as follows:
X = number of bases
1
2
3
4
P(X)
0.706
0.150
0.006
0.138
Calculate the standard deviation of X.
11. Find the Z-value with an area of 0.0256 under the standard normal curve to its left.
12. Find the Z-value with an area of 0.8051 under the standard normal curve to its right.
13. Assume that the random variable X is normally distributed with mean μ = 120 and standard
deviation σ = 13. Find P(100 < X < 155).
14. Problem #42 on page 325
4. In a national highway Traffic Safety Administration (NHTSA) report, data provided to the
NHTSA by Goodyear stated that the mean tread life of a properly inflated automobile tires
is 45,000 miles. Suppose that the current distribution of tread life of properly inflated
automobile tires is normally distributed with mean of 45,000 miles and a standard deviation
of 2360 miles.
a. Find the probability that randomly selected automobile tire has a tread life between
42,000 and 46,000 miles.
b. Find the probability that randomly selected automobile tire has a tread life of more than
50,000 miles.
c. Find the probability that randomly selected automobile tier has a tread life of less than
38,000 miles.
d. Suppose that 6% of all automobile tires with the longest tread life have tread life of at
least x miles. Find the value of x.
e. Suppose that 2% of all automobile tires with the shortest tread life have tread life of at
most x miles. Find the value of x.
5. Heights for college women are normally distributed with mean 65 inches and standard
deviation 2.7 inches.
a. Find the probability of college women whose heights fall between 62 inches and 65
inches.
b. Find the probability of college women whose heights fall less than 70 inches.
c. Find the probability of college women whose heights fall greater than 60 inches.
d. Find the height such that about 25% of college women are shorter than that height.
e. Find the heights that mark off the middle 90% of heights.
6. Suppose the yearly rainfall totals for a city in northern California follows a normal
distribution with mean of 18 inches and a standard deviation of 6 inches. For a randomly
selected year, what is the probability that total rainfall will be in each of the following
interval.
a. Less than 10 inches.
b. Greater than 30 inches.
c. Between 15 and 21 inches.