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MAT 155 Sample Test for Chapter 5: Discrete Probability Distributions and
Chapter 6: Normal Probability Distributions
Dr Moore
INSTRUCTIONS: Read each statement and problem carefully. Perform calculations, as necessary.
Show all necessary work.
For Problems 1 and 2, assume that voltages in a circuit vary between 5 volts and 11 volts, and voltages are
spread evenly over the range of possibilities (Uniform Distribution). Find the probability of the given
range of voltage levels. [Make a sketch for each problem.]
1. Greater than 9 volts
2.
Between 5.5 volts and 10 volts
For Problems 3, 4, 5, and 6, assume that the readings on the thermometers are normally distributed with a mean
of 0C and a standard deviation of 1.00C. [Make a sketch for each problem.]
3. Find the indicated probability where z is the reading in degrees: P(z < 1.645)
4. Find the indicated probability where z is the reading in degrees: P(1.96 < z < 2.33)
5. Find the temperature reading corresponding to P20, the 20th percentile.
6. If 12% of the thermometers are rejected because they have readings that are too high, but all other
thermometers are acceptable, find the reading that separates the rejected thermometers from the others.
[Make a sketch for each problem.]
For Problems 7, 8, 9, and 10, assume that women’s weights are normally distributed with a mean given by
 = 143 lbs and standard deviation given by  = 29 lbs. Also, assume that a woman is randomly selected.
Let x = weight in pounds.
7. Find the indicated probability: P(150 < x < 180)
8. Find the indicated probability: P(x < 186.5)
9. Find the sixth decile, D6, which is the weight separating the bottom 60% from the top 40%.
10. a) If 1 woman is randomly selected, find the probability that her weight is above 140 lb.
b) If 100 women are randomly selected, find the probability that they have a mean weight greater than 140
lb.
11. The U.S. Army requires women’s heights to be between 58 in. and 80 in. Find the percentage of women
meeting that height requirement. Are many women being denied the opportunity to join the Army because
they are too short or too tall? [Assume that heights of women are normally distributed with a mean of  =
63.6 in. and a standard deviation of  = 2.5 in.]
12. The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15
days. If we stipulate that a baby is premature if born at least three weeks early, what percentage of babies is
born prematurely?
For Problems 13 and 14, use the fact that IQ scores are normally distributed with a mean of 100 and a standard
deviation of 15. [Make a sketch for each problem.]
13. a) People are considered to be “intellectually very superior” if their score is above 130. What percentage of
people fall into that category?
b) If we redefine the category of “intellectually very superior” to be scores in the top 2%, what does the
minimum score become?
14. If 25 people are randomly selected for an IQ test, find the probability that their mean IQ score is between
95 and 105.
15. Assume that a computer or calculator was used to generate the given confidence interval limits. Find the (a)
the mean x and (b) the margin of error E. Confidence interval: 2.17 <  < 2.57
16. Find the critical value z that corresponds to the 92% degree of confidence. [Make a sketch for each
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problem.]
17. Using the 99% level of confidence, find the (a) margin of error E and (b) the confidence interval for the
population mean  for times between uses of a TV remote control by males during commercials. Use the
sample data n = 150, x = 7.60 sec, and s = 2.72 sec.
18. Given the sample data n = 100,  = 4.2, and the population appears to be very skewed. Use the 99% level
of confidence to find the appropriate critical value (a) t or (b) z or (c) state that neither the normal nor
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the t-distribution applies.
19. Use the given data from final exam test scores in a statistics course to find the 95% confidence interval: n =
27, x = 78.8, and s = 12.2.
20. In crash tests of 15 Honda Odyssey minivans, collision repair costs are found to have a distribution that is
roughly bell-shaped, with a mean of $1786 and a standard deviation of $937. Construct the 99% confidence
interval for the mean repair cost in all such vehicle collisions.
21. To plan for the proper handling of household garbage, the city of Providence must estimate the mean
weight of garbage discarded by households in one week. Find the sample size necessary to estimate that
mean if you want to be 96% confident that the sample mean is within 2 lbs of the true population mean. For
the population standard deviation , use the value 12.46 lbs, which is the standard deviation of the sample
of 62 households included in the Garbage Project study conducted at the University of Arizona.
22. Assume that a sample is used to estimate a population proportion p. Find the margin of error E that
corresponds to the given statistics and the degree of confidence: n= 1000 and x = 250 at the 98% level of
confidence.
23. For a sample of size n = 1200 and x = 800, construct the 90% confidence interval estimate of the population
proportion p.
24. Use the given data to find the minimum sample size required to estimate a population proportion or
percentage. Margin of error is three percentage points, confidence level is 95%, and sample proportion is
estimated to be 0.15 from a prior study.
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