Question

Teacher's salaries in Georgia are normally distributed with an average salary of $52,000 with a standard deviation of $12,000. What percentage of teachers earn an a salary between $40,000 and $76,000?

Answer 1

81.85%

Explanation:

We have the following information:

mean = m = 52000

standard deviation = sd = 12000

a = 40000

b = 76000

we need to find the probability between a and b, that is:

P (a <x <b) = P (40,000 <x <76000)

P [(40000 - m) / sd <(x - m) / sd <(76000 - m) / sd]

replacing

P [(40000 - 52000) / 12000 <z <(76000 - 52000) / 12000]

P (-1 <z <2)

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

We look for this value of z, in the attached table:

0.9772 - 0.1587

P = 0.8185

In other words, the probability is 81.85%