Probability of a Sample population

Question

A survey of 500 randomly selected customers based on their expenditure patterns was carried out and the data were found to be normally distributed with a mean of N50 and a standard deviation of N15. Use the information to answer the following questions:

The probability that any customers are selected at random:

a)         spends more than N80 per week,

           b)    spends less than N50 per week.

The percentage of customers who are expected to:

           c)    spend between N30 and N80 per week,

           d)    spend between N55 and N70 per week.

The expected number of customers who will:

           e)   spend less than N70 per week,

           f)    spend between N37.50 and N57.50 per week.

Answer 1

(80-50)/15 = 2 standard deviations above the mean

by the empirical rule that's 95% within 2 standard deviations of the mean

95/2 = 47.5% above 80

Less than 50 is 50%. Half are above and half below the mean