Question

According to the IRS Stats of income bulletin charitable contributions itemized per income tax return in Pennsylvania are normally distributed with a mean of $792 and a standard deviation of $103. What are the limits (max, min) for the middle 50% of contributions

Plz show work throughly

Answer 1

Solution :

mean = = $792

standard deviation = =$103

Using standard normal table,

P(-z < Z < z) = 50%
P(Z < z) - P(Z < z) = 0.50
2P(Z < z) - 1 = 0.50
2P(Z < z ) = 1 + 0.50
2P(Z < z) = 1.50
P(Z < z) = 1.50 / 2
P(Z < z) = 0.75
z = 0.67 znd z = - 0.67

Using z-score formula,

x = z * +

x = 0.67 * 103 + 792

= 861.01

The maximum limits = 861.01

x = z * +

x = - 0.67 *103 + 792

= 722.99

The maximum limits = 722.99