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Homework Assignments (100 points)

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

randomly.

a. Determine the standard error of the proportion.

b. What is the probability that the sample proportion of females is between .40 and .55?

2. The average lifetime of a light bulb is 3,000 hours with a standard deviation of 696 hours. A

simple random sample of 36 bulbs is taken.

a.

What are the expected value, standard deviation, and shape of the sampling distribution

of ?

b. What is the random variable in this problem? Define it in words.

c. What is the probability that the average life in the sample will be between 2,670.56 and

2,809.76 hours?

d. What is the probability that the average life in the sample will be greater than 3,219.24

hours?

e. What is the probability that the average life in the sample will be less than 3,180.96 hours?

3. A population of 1,000 employees spends an average of $10.50 a day on dinner. The standard

deviation of the expenditure is $3. A simple random sample of 64 students is taken.

a.What are the expected value, standard deviation, and shape of the sampling distribution

of the sample mean?

b.What is the probability that these 64 students will spend a combined total of more than

$715.21?

c.What is the probability that these 64 students will spend a combined total between

$703.59 and $728.45?

4. In a restaurant, the proportion of people who order coffee with their dinner is .9. A simple

random sample of 144 patrons of the restaurant is taken.

a.

What are the expected value, standard deviation, and shape of the sampling distribution

of ?

b. What is the random variable in this problem? Define it in words.

c. What is the probability that the proportion of people who will order coffee with their

meal is between .85 and .875?

d. What is the probability that the proportion of people who will order coffee with their meal is at least .945?