Complete the mcq:
Find the indicated probability or percentage for the normally distributed variable.
1) The variable X is normally distributed.The mean is µ = 22.0 and the standard deviation is Η = 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 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 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 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 ? that corresponds to a confidence level of 84%.
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) Η = 16, construct a 95.44% confidence interval for the mean score, µ, 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 Η = 23 hours. Construct a 90% confidence interval for the mean life, µ, 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 µ. Which of the following statements 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 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 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 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 2