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1. Using Table A, find the proportion of observations from a standard normal distribution that satisfies each of
the following statements. In each case, sketch the normal curve and shade the area under the curve that is
the answer to the question.
a) Z < –1.5
b) 0.8 < Z < 1.5
2. Runners competed in a local road race. The mean finishing time for the race was 43.5 minutes with a
standard deviation of 16.2 minutes. The sponsors wanted to have a special race for those who were in the
fastest 10%. Assuming the times are normally distributed, which of the following is the cutoff time?
(Caution: which are the fastest 10% of all the times, the top 10% of the distribution or the bottom 10%?)
a)
22.8 minutes
b)
25.7 minutes
c)
39.2 minutes
d)
42.2 minutes
e)
64.3 minutes
3. When is the mean of a density curve equal to the median? When is the mean of a density curve greater than
the median?
4. In a normal distribution, what percent of the observations lie within 1 standard deviation on either side of
the mean?
In a normal distribution, what percent of the observations lie within 2 standard deviation on either side of
the mean?
In a normal distribution, what percent of the observations lie within 3 standard deviation on either side of
the mean?
In a normal distribution, what percent of the observations lie within 2.24 standard deviation on either side of
the mean?
5. Researchers in Norway analyzed data on the birth weights of 400,000 newborns over a 6-year period. The
distribution of birth weights is normal with a mean of 3668 grams and a standard deviation of 511 grams.
Babies that weigh less than 2500 grams at birth are classified as “low birth weight.” What percent of babies
will be identified as low birth weight?
6. How many standard deviations above the mean do you need to be in order to be in the top 25% for height
for people your age?
7. The height of 3-year-old boys is approximately normally distributed. Keziah and Randy are 3-year-old boys.
Keziah is 32.0 inches tall and is at the 32nd percentile of the distribution. Randy is 34.0 inches tall and is at
the 62nd percentile of the distribution. Which of the following is closest to the mean of the height
distribution?
a. 32.50 inches
b. 32.79 inches
c. 33.00 inches
d. 33.21 inches
e. 36.53 inches.
8. In a large set of data that are approximately normally distributed,
r is the value in the data set that has a z-score of -1.00,
s is the value of the first quartile, and
t is the value of the 20th percentile.
Which of the following is the correct order from least to greatest for the values of r, s, and t?
a. r, s, t
b. r, t, s
c. s, t, r
d. t, r, s,
e. t, s, r
9.
Solutions:
1. a) 0.0668 b) 0.1451
2. (a)
3. when the density curve is symmetric, when the density curve is skewed right
4. 68%, 95%, 99.7%, 97.5%
5. 1.1%
6. 0.67 standard deviations above the mean
7. D
8. B
9. a) median = approximately 21 cents per gallon, IQR = approximately 7 cents per gallon
b) median = approximately 39.4 cents per gallon, IQR = approximately 7 cents per gallon