Question

The average teacher’s salary in Connecticut is $57,337. Suppose that the distribution of salaries is normal with a population standard deviation of $7500.
(a) What is the probability that a randomly selected teacher makes less than $56,000 per year?

(b) If we sample 100 teachers’ salaries, what is the probability that the sample mean is less than $56,000?

Answer 1

Solution :

Given that ,

mean = = 57337

standard deviation = = 7500

( a ) P(x < 56000 ) = P[(x - ) / < ( 56000 -57337 ) / 7500]

= P(z < -0.18 )

Using z table,

= 0.4286

probability = 0.4286

( b )

n = 100

= 57337

= / n = 7500 / 100 =750

P( < 56000 ) = P ( - ) / < ( 56000 - 57337 ) / 750 )

= P( z < -1.78)

Using z table

= 0.0375   

Probability = 0.0375