Question

The average starting salary of this year’s graduates of a large university (LU) is $20,000 with a standard deviation of $8,000. Furthermore, it is known that the starting salaries are normally distributed.

1.What is the maximum starting salary of the middle 39.70% of the LU graduates?

2.Individuals with starting salaries of less than $12,480 receive a low income tax break. What percentage of the graduates will receive the tax break?

3.What is the minimum starting salary of the middle 90% of the LU graduates?

Answer 1

Solution :

Given that,

mean = = 20,000

standard deviation = = 8,000

Using standard normal table,

1 ) P(-z < Z < z) = 39.70%
P(Z < z) - P(Z < z) = 0.397
2P(Z < z) - 1 = 0.397
2P(Z < z ) = 1 + 0.397
2P(Z < z) = 1.397
P(Z < z) = 1.397 / 2
P(Z < z) = 0.6985
z = 0.52 and z = - 0.52

Using z-score formula,

x = z * +

x = 0.52 * 8,000 +20,000

x = 24160

x = z * +

x = -0.52 * 8,000 +20,000

x = 15840

2 ) P( x < 12,480 )

P ( x - / ) < ( 12,480 - 20000 / 8000)

P ( z < -7520 /8000 )

P ( z < -0.94 )

= 0.1736

Probability = 0.1736 = 17.36%

3 ) P(-z < Z < z) = 90%
P(Z < z) - P(Z < z) = 0.90
2P(Z < z) - 1 = 0.90
2P(Z < z ) = 1 + 0.90
2P(Z < z) = 1.90
P(Z < z) = 1.90 / 2
P(Z < z) = 0.95
z = 1.64 and z = - 1.64

Using z-score formula,

x = z * +

x = 1.64 * 8,000 +20,000

x = 33120

x = z * +

x = -1.64 * 8,000 +20,000

x = 6880