Question

Rochester, New York, averages μ = 21.9 inches of snow for the month of December. The distribution of snowfall amounts is approximately normal with a standard deviation of σ = 6.5 inches. This year, a local jewelry store is advertising a refund of 50% off all purchases made in December, if the accumulated snowfall by the end of the month falls within the top 10% of the distribution. How many inches of snow have to fall for the jewelry store to have to pay off on its promise?

Answer 1

Solution:-

Given that,

mean = = 21.9

standard deviation = = 6.5

Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.28 ) = 0.90  

z = 1.28

Using z-score formula,

x = z * +

x = 1.28 * 6.5 + 21.9

x = 30.22 inches.