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CHAPTER 7 REVIEW
FORM A
1. Each of the following curves fails to be a normal curve. Why?
(a)
1. (a) __________________________
(b)
(b) __________________________
2. According to the empirical rule, for a distribution that is
symmetrical and bell-shaped, approximately _______ of
the data values will lie within three standard deviations on
each side of the mean.
2. ______________________________
3. Assuming that the heights of boys in a high school basketball tournament are normally distributed, with mean 70 inches
and standard deviation 2.5 inches, how many boys in a group
of 40 do we expect to be taller than 75 inches?
3. _____________________________
4.Let x be a random variable that represents the length of time
it takes a student to complete Dr. Gill’s chemistry lab project.
From long experience, it is known that x has a normal distribution with mean  = 3.6 hours and standard deviation  = 0.5
hour.
Convert each of the following x intervals to standard z intervals.
(a) x  4.5
4. (a) __________________________
(b) 3  x  4
(b) __________________________
(c) x  2.5
(c) __________________________
(#4 continued)
Convert each of the following z intervals to raw score x intervals.
(d) z  1
(d) __________________________
(e) 1  z  2
(e) __________________________
(f) z  1.5
(f) __________________________
5. John and Joel are salesmen in different districts. In
John’s district, the monthly mean sale is $17,319
with standard deviation $684. In Joel’s district, the
monthly mean sale is $21,971 with standard deviation
$495. Assume that sales in both districts follow a
normal distribution.
(a) Last month John sold $19,214 whereas Joel
sold $22,718 worth of merchandise. Relative
to the buying habits of customers in each
district, does this mean Joel is a better salesman? Explain.
5. (a) __________________________
____________________________
(b) Convert Joel’s sales last month to a standard
z score, and do the same for John’s sales last
month. Who do you think is
the better salesman?
(b) __________________________
6. The length of time to complete a door assembly on
an automobile factory assembly line is normally distributed with mean  = 6.7 minutes and standard
deviation  = 2.2 minutes. For a door selected at
random, what is the probability the assembly line
time will be
(a) 5 minutes or less?
6. (a) __________________________
(b) 10 minutes or more?
(b) __________________________
(c) between 5 and 10 minutes?
(c) __________________________
7. From long experience, it is known that the time it takes
to do an oil change and lubrication job on a vehicle has
a normal distribution with mean  = 17.8 minutes and
standard deviation  = 5.2 minutes. An auto service shop
will give a free lube job to any customer who must wait
beyond the guaranteed time to complete the work. If the
shop does not want to give more than 1% of its customers
a free lube job, how long should the guarantee be (round
to the nearest minute).
7. _____________________________
8. Medical treatment will cure about 87% of all people who
suffer from a certain eye disorder. Suppose a large medical
clinic treats 57 people with this disorder. Let r be a random
variable that represents the number of people that will recover.
The clinic wants a probability distribution for r.
(a) Estimate P  r  47  .
(a) __________________________
(b) Estimate P  47  r  55 .
(b) __________________________
9. The diameters of oranges from a Florida orchard are normally
distributed with mean  = 3.2 inches and standard deviation
 = 1.1 inches. A packing supplier is designing special occasion
presentation boxes of oranges and needs to know the average
diameter for a random sample of 8 oranges. What is the probability that the mean diameter x for a sample of 8 oranges is
(a) smaller than 3 inches?
9. (a) __________________________
(#9 continued)
(b) larger than 3.5 inches?
(b) __________________________
(c) between 3.1 and 3.3 inches?
(c) __________________________
10. The manufacturer of a new compact car claims the miles per
gallon (mpg) for the gasoline consumption is mound shaped
and symmetrical with mean  = 25.9 mpg and standard deviation
 = 9.5 mpg. If 30 such cars are tested, what is the probability
the average mpg x is
(a) less than 23 mpg?
10. (a) __________________________
(b) greater than 28 mpg?
(b) __________________________
(c) between 23 and 28 mpg?
(c) __________________________