Question

Itemized Charitable ContributionsThe average charitable contribution itemized per income tax return in Pennsylvania is $792 Suppose that the distribution of contributions is normal with a standard deviation of $103. Find the limits for the middle 66% of contributions?

Answer 1

Solution:-

Given that,

mean = = 792

standard deviation = = 103

Using standard normal table,

P( -z < Z < z) = 66%

= P(Z < z) - P(Z <-z ) = 0.66

= 2P(Z < z) - 1 = 0.66

= 2P(Z < z) = 1 + 0.66

= P(Z < z) = 1.66 / 2

= P(Z < z) = 0.83

= P(Z < 0.95 ) = 0.83

= z  ± 0.95

Using z-score formula,

x = z * +

x = -0.95 * 103 + 792

x = $ 694.15

Using z-score formula,

x = z * +

x = 0.95 * 103 + 792

x = $ 889.85

The middle 66% are from $ 694 to $ 890