Question

3.   Sampling and Sampling Distributions

The Sugary Drinks Portion Cap Rule, also known as the Soda Ban was passed to help limit the sale of sweetened drinks.  Analyzing the effectiveness, data was collected which indicated the per capita consumption of soda is 2.3 gallons per month.  Assume the standard deviation for the population is 0.75 gallons per month.  A random sample of 36 individuals.

a.   What is the probability that the sample mean will be less than 2.1 gallons per month?

b.   What is the probability that the sample mean will be more than 2.2 gallons per month?

c.   Identify the symmetrical interval that includes 95% of the mean if the true population mean is 2.3 gallons per month.

4.   Sampling and Sampling Distributions

In the most recent hearing on Highway safety at the New York City Council hearings, it was determined that the average travels 1,123 miles per month.  Assume the population standard deviation is 341 miles per month. Determine the interval that will contain 95% of the sample means for the sample size of

a. 30 drivers

b. 45 drivers

c. Explain the difference in these probabilities

Answer 1

a)

The following information about the mean and standard deviation has been provided:

We need to compute . The corresponding z-value needed to be computed is:

Therefore, we get that

b)

The following information about the mean and standard deviation has been provided:

We need to compute . The corresponding z-value needed to be computed is:

Therefore, we get that

c)

For 95% Confidence interval, z_c= 1.96

CI = ( 2.3 - 0.245 , 2.3 + 0.245 )

CI = ( 2.055 , 2.545 )