Hi, please answer all the questions and show work. I need it by 8:30pm. Thank you.

1. The number of hours spent on household chores by all adults has a mean of 27.3 hours and a standard deviation of 9.5 hours per week. One wants to find the probability that the mean number of hours spent for household chores by a sample of 40 adults will be more than 26.75.

What is the z-score that needs to be computed to find the probability? Find the z-score only (rounded to 2 decimal places.)

z =

2. Each year, the US vehicle market shows that among all sales, the proportion of new vehicles sold, is about 33%.

A sample of 200 vehicles is selected for a further study. One wants to find the probability that the sample proportion is greater than 40%.

Check the requirements in order to use a normal distribution for the probability. You don't need to compute the probability but show the requirement check.

(You may write it in words.)

3. The Food Marketing Institute shows that 17% of households spend more than $100 per week on groceries. Assume that the population proportion is P = .17 and a sample of 700 households will be selected from the population.

Answer the following questions. The requirements to use the normal distribution, are satisfied.

A. Calculate sigma subscript p with bar on top end subscript the standard error of the proportion of households spending more than $100 per week on groceries (to 4 decimals).

B. What is the probability that the sample proportion will be within +/- .03 of the population proportion (to 4 decimals)?

Find the values of z-scores first.

A. sigma subscript p with bar on top end subscript (rounded to 4 decimal places):

B. a. Z-scores (rounded to 2 decimal places) :

b. The probability (rounded to 4 decimal places) :

Identify whether the following statement is true.

4. A z-score is a number of standard deviation from the mean of the distribution.

A. True

B. False

C. It is different for each case.