The IRS reports that the mean refund for a particular group of taxpayers was $1,600. The distribution of tax refunds follows a normal distribution with a standard deviation of $850. Required:
a. What percentage of the refunds are between $1,600 and $2,000?
b. What percentage of the refunds are between $900 and $2,000?
c. What percentage of the refunds are between $1,800 and $2,000?
d. Ninety-five percent of the refunds are for less than what amount?

The monthly demand equation for an electric utility company is estimated to be p equals 60 minus left parenthesis 10 superscript negative 5 baseline right parenthesis x, where p is measured in dollars and x is measured in thousands of killowatt-hours. the utility has fixed costs of $3 comma 000 comma 000 per month and variable costs of $32 per 1000 kilowatt-hours of electricity generated, so the cost function is upper c left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 32 x. (a) find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) suppose that the rising fuel costs increase the utility's variable costs from $32 to $38, so its new cost function is upper c 1 left parenthesis x right parenthesis equals 3 times 10 superscript 6 baseline plus 38 x. should the utility pass all this increase of $6 per thousand kilowatt-hours on to the consumers?