4) The manager of a soda bottling plant has determined that the mean amount of s

Question

4) The manager of a soda bottling plant has determined that the mean amount of soda in 12-ounce cans produced at the plant is 12.1 ounces with a standard deviation of .2 ounces. As part of the quality control program, the manager takes a random sample of 64 cans and calculates the sample mean.
a) What is the sampling distribution of the mean?

b) What is the probability that the sample mean is less than 12.05 ounces?
c) What is the probability that the sample mean is greater than 12.075 ounces?
d) The manager is concerned about the time and money spent taking samples of size 64. If the manager

wanted to sample only 16 cans, what advice would you give the manager?

Explanation / Answer

4) The manager of a soda bottling plant has determined that the mean amount of soda in 12-ounce cans produced at the plant is 12.1 ounces with a standard deviation of .2 ounces. As part of the quality control program, the manager takes a random sample of 64 cans and calculates the sample mean.
a) What is the sampling distribution of the mean?

Mean of sampling distribution =12.1

Sd of the sampling distribution =0.2/sqrt(64) =0.025

b) What is the probability that the sample mean is less than 12.05 ounces?

Z value for 12.05, z=(12.05-12.1)/0.025 = -2

P( mean x < 12.05) = P( z < -2) = 0.0228

c) What is the probability that the sample mean is greater than 12.075 ounces?

Z value for 12.075, z=(12.075-12.1)/0.025 = -1

P( mean x > 12.075) = P( z > -1) = 0.8413

d) The manager is concerned about the time and money spent taking samples of size 64. If the manager wanted to sample only 16 cans, what advice would you give the manager?

If the sample size decreases from 64 to 16, the standard error will increase to 0.05.

The result accuracy may be decreased.

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