Question

The salaries of teachers in the West Bloom Field Public School District are normally distributed with a mean of $53.5 thousand with a standard deviation of 5.5. What is the probability that a sample of 20 teachers will have a salary:

1. Above 53.5?
2. Below 50?
3. Above 55?
4. Between 54 and 55?

Answer 1

μ =53500

σ =5500

n= 20

Z=X-μ/(σ/√n)

A)

P(X>53500)

=P(z > 53500-53500/(5500/√20))

=P(z > 0)

=0.5 [standard normal distribution table]

B)

P( X < 50000)

= P( z < 50000-53500/(5500/√20))

=P(z < -2.84)

=0.5-0.4977 [standard normal distribution table]

=0.0023

C)

P(x > 55000)

=P( z > 55000-53500/(5500/√20))

=P(z > 1.22)

=0.5-0.3888 [standard normal distribution table]

=0.1112

D)

P(54000 < x < 55000)

=P( 54000 -53500/(5500/√20) < z < 55000-53500/(5500/√20) )

=P(0.41 < z < 1.22)

=0.3888 - 0.1591 [ standard normal distribution table]

=0.2297