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# 11 Probability questions

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Find the indicated probability or percentage for the normally distributed variable.
1) The variable X is normally distributed.The mean is &#956; = 22.0 and the standard deviation is &#56256;&#57239; = 2.4. 1)
Find P(19.7 < X < 25.3).

A) 0.4107 B) 1.0847 C) 0.3370 D) 0.7477

2) The incomes of trainees at a local mill are normally distributed with a mean of \$1,100 and a 2)
standard deviation \$150. If a sample of 100 trainees is selected, what is the probability that the
sample mean will be less than \$1075 a month?
A) 4.478% B) 43.38% C) 35.31% D) 90.82%

Use the empirical rule to solve the problem.
3) The lifetimes of lightbulbs of a particular type are normally distributed with a mean of 290 hours 3)
and a standard deviation of 6 hours. What percentage of the bulbs have lifetimes that lie within 1
standard deviation to either side of the mean?
A) 68.26% B) 31.74% C) 84.13% D) 95.44%

4) The amount of Jen's monthly phone bill is normally distributed with a mean of \$53 and a standard 4)
deviation of \$10. What percentage of her phone bills are between \$23 and \$83?
A) 99.99% B) 99.74% C) 95.44% D) 68.26%

Provide an appropriate response.

5) Find the value of &#56256;&#57221; that corresponds to a confidence level of 84%. 5)
A) 0.84 B) 0.16 C) 16 D) 0.016
Find the confidence interval specified.
6) The mean score, x, on an aptitude test for a random sample of 9 students was 64. Assuming that 6)
&#56256;&#57239; = 16, construct a 95.44% confidence interval for the mean score, &#956;, of all students taking the test.
(HINT: Think of the empirical rule.)
A) 53.3 to 74.7 B) 60.4 to 67.6 C) 32 to 96 D) 56.0 to 72.0
7) A random sample of 108 light bulbs had a mean life of x = 479 hours. Assume that &#56256;&#57239; = 23 hours. 7)
Construct a 90% confidence interval for the mean life, &#956;, of all light bulbs of this type.
A) 475.3 to 482.7 hours B) 474.7 to 483.3 hours
C) 473.3 to 484.7 hours D) 473.8 to 484.2 hours
1
Provide an appropriate response.
8) Suppose you have obtained a 95% confidence interval for &#956;.Which of the following statements 8)
is/are true regarding the relationship between precision and confidence level? Assume that the
sample size is fixed.
A. Increasing the confidence level to 99% will result in a narrower interval.
B. Decreasing the confidence level to 90% will result in greater precision.
C. Decreasing the precision will result in a higher confidence level.
D. Increasing the precision will result in a higher confidence level.
A) A and D B) B and C C) B and D D) A and C
9) Suppose that you wish to obtain a confidence interval for a population mean. Under the conditions 9)
described below, should you use the z-interval procedure, the t-interval procedure, or neither?
- The population standard deviation is unknown.
- The population is normally distributed.
- The sample size is small.
A) t-interval procedure B) Neither C) z-interval procedure
Find the confidence interval specified. Assume that the population is normally distributed.
10) A laboratory tested twelve chicken eggs and found that the mean amount of cholesterol was 186 10)
milligrams with s = 19.0 milligrams. Construct a 95% confidence interval for the true mean
cholesterol content of all such eggs.
A) 173.8 to 198.2 milligrams B) 176.1 to 195.9 milligrams
C) 174.0 to 198.0 milligrams D) 173.9 to 198.1 milligrams
11) Thirty randomly selected students took the calculus final. If the sample mean was 90 and the 11)
standard deviation was 13.9, construct a 99% confidence interval for the mean score of all students.
A) 83.01 to 96.99 B) 83.03 to 96.97 C) 83.75 to 96.25 D) 85.69 to 94.31