Ex 9.3.2

1. An automotive repair shop has determined that the average service time on an automobile

is 2 hours with a standard deviation of 32 minutes. A random sample of 64 services

is selected.

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(a) What is the probability that the sample of 64 will have a mean service time

greater than 114 minutes? (to 4 digits)

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(b) Assume the population consists of 400 services. Determine

the standard error of the mean. (to 2 digits)

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2. In a large university, 20% of the students are business majors. A random sample of

100 students is selected, and their majors are recorded.

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(a) Compute the standard error of the proportion.

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(b) What is the probability that the sample contains at least 12 business majors?

(to 4 digits)

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(c) What is the probability that the sample contains between 12 and 14 business majors?

(to 3 digits)

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(d) What is the probability that the sample contains less than 15 business majors?

(to 4 digits)

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3. The average daily earnings of bus drivers in a city is $950 with a standard deviation $45.

Assume that we select a random sample of 81 bus drivers from a population of 400 drivers.

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(a) What is the standard error of the mean? (to 2 digits)

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(b) What is the probability that the sample mean will be greater than $960? (to 4 digits)

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4. There are 500 employees in a firm, 45% are female. A sample of 60 employees is

selected randomly.

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(a) Determine the standard error of the proportion. (to 4 digits)

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(b) What is the probability that the sample proportion of females is between 0.4 and 0.55?

(to 4 digits)

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