Question

The number of gallons of milk sold in a day in a grocery store is approximately normally distributed with a mean of 600 gallons and a standard deviation of 50 gallons. By the Empirical Rule:

a. for approximately 68% of the days, between 500 and 700 gallons of milk are sold

b. for approximately 75% of the days, between 500 and 700 gallons of milk are sold

c. for approximately 95% of the days, between 500 and 700 gallons of milk are sold

d. for approximately 99.7% of the days, between 500 and 7000 gallons of milk are sold

Answer 1

Solution :

Given that,

mean = = 600

standard deviation = = 50

Using Empirical rule,

P( - 2 < x <   + 2 ) = 95%

= P( 600 - 2 * 50 < x < 600 + 2 * 50 ) = 95%

= P( 600 - 100 < x < 600 + 100 ) = 95%

=P( 500 < x < 700 ) = 95%

c. for approximately 95% of the days, between 500 and 700 gallons of milk are sold