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Math 227 Sec 6.2
Name___________________________________
Using the following uniform density curve, answer the question.
1) What is the probability that the random variable has a value greater than 5?
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 of the given range of
pounds lost.
2) More than 10 pounds
Find the area of the shaded region. The graph depicts the standard normal distribution with mean 0 and standard
deviation 1.
3)
4)
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Find the indicated z score. The graph depicts the standard normal distribution with mean 0 and standard deviation 1.
5) Shaded area is 0.9599.
6) Shaded area is 0.4013.
If z is a standard normal variable, find the probability.
7) The probability that z lies between 0 and 3.01
8) P(-0.73 < z < 2.27)
Find the indicated value.
9) z 0.005
10) z 0.36
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Math 227 Sec 6.3
Name___________________________________
Provide an appropriate response.
1) Find the area of the shaded region. The graph depicts IQ scores of adults, and those scores are normally
distributed with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
A) 0.4400
B) 0.7486
C) 0.6293
D) 0.8051
2) Find the indicated IQ score. The graph depicts IQ scores of adults, and those scores are normally distributed
with a mean of 100 and a standard deviation of 15 (as on the Wechsler test).
The shaded area under the curve is 0.10.
A) 100.5
B) 80.8
C) 119.2
D) 108.1
3) Assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard deviation of
15 (as on the Wechsler test). Find P30, which is the IQ score separating the bottom 30% from the top 70%.
A) 92.8
B) 91.9
C) 92.2
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D) 91.4
Solve the problem. Round to the nearest tenth unless indicated otherwise.
4) In one region, the September energy consumption levels for single-family homes are found to be normally
distributed with a mean of 1050 kWh and a standard deviation of 218 kWh. Find P45, which is the consumption
level separating the bottom 45% from the top 55%.
A) 1148.1
B) 1021.7
C) 1087.8
D) 1078.3
5) Assume that women have heights that are normally distributed with a mean of 63.6 inches and a standard
deviation of 2.5 inches. Find the value of the quartile Q3 .
A) 65.3 inches
B) 67.8 inches
C) 66.1 inches
Assume that X has a normal distribution, and find the indicated probability.
6) The mean is µ = 60.0 and the standard deviation is = 4.0.
Find the probability that X is less than 53.0.
A) 0.9599
B) 0.0802
C) 0.5589
D) 64.3 inches
D) 0.0401
Find the indicated probability.
7) The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.30 inches and a
standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.32 inches?
A) 97.72%
B) 2.28%
C) 47.72%
D) 37.45%
8) The weekly salaries of teachers in one state are normally distributed with a mean of $490 and a standard
deviation of $45. What is the probability that a randomly selected teacher earns more than $525 a week?
A) 0.1003
B) 0.2823
C) 0.2177
D) 0.7823
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