Data are uniformly distributed between the values of 6 and 14. Determine the value of f (x).**(a)** What are the mean and standard deviation of this distribution?**(b)** What is the probability of randomly selecting a value greater than 11?**(c)** What is the probability of randomly selecting a value between 7 and 12?

Round your answers to 3 decimal places, the tolerance is +/-0.001

**(a)**

f(x) = [removed]

μ = [removed]

σ = [removed]

**(b)**

P(x > 11) = [removed]

**(c)**

P(7 < x < 12) = [removed]

According to the Internal Revenue Service, income tax returns one year averaged $1,332 in refunds for taxpayers. One explanation of this figure is that taxpayers would rather have the government keep back too much money during the year than to owe it money at the end of the year. Suppose the average amount of tax at the end of a year is a refund of $1,332, with a standard deviation of $725. Assume that amounts owed or due on tax returns are normally distributed.**(a)** What proportion of tax returns show a refund greater than $2,000?**(b)** What proportion of the tax returns show that the taxpayer owes money to the government?**(c)** What proportion of the tax returns show a refund between $100 and $700?

Round z values to 2 decimal places. Round your answers to 4 decimal places.

**(a)**

P(x > $2000) = [removed]

**(b)**

P(x < 0) = [removed]

**(c)**

P($100 < x < $700) = [removed]

The average cost of a one-bedroom apartment in a town is $550 per month. What is the probability of randomly selecting a sample of 50 one-bedroom apartments in this town and getting a sample mean of less than $530 if the population standard deviation is $100?

Round the values of *z* to 2 decimal places. Round your answer to 4 decimal places, the tolerance is +/-0.0001.

[removed]

The net profit from a certain investment is normally distributed with a mean of $10,000 and a standard deviation of $5,000. The probability that the investor will not have a net loss is ____________.