1. Studen ts of a large university spend an average of S5 a day on lunch. The st

Question

1. Studen ts of a large university spend an average of S5 a day on lunch. The standard deviation of the expenditure is $3. A simple random sample of 36 students is taken. a. What is the sampling distribution of the sample mean? b. What is the probability that the sample mean will be at least $6? What is the probability that the sample mean will be less than $10? c. 2. 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. What are the expected value, standard deviation, and shape of the sampling distribution of P? a. What is the probability that the proportion of people who will order coffee with their meal is between 0.85 and 0.875? b. What is the probability that the proportion of people who will order coffee with their meal is at least 0.945? c.

Explanation / Answer

a) sample mean is same as population mean

so sample mean =5

b)

=5

=3

n=36

x=6

z=(x-)/(/n)

=(6-5)/(3/36)

=1/(3/6)

=1/0.5

=2

P(x> 6) =P(z>2)

              =1-P(z<2)

              =1 - 0.9772

              =0.0228

c) P(x<10)

=5

=3

n=36

x=10

z=(x-)/(/n)

=(10-5)/(3/36)

=5/(3/6)

=5/0.5

=10

P(x<10) =P(z<10) =1

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