Question

For certain​ workers, the mean wage is $6.50​/hr, with a standard deviation of ​$0.25 If a worker is chosen at​ random, what is the probability that the​ worker's wage is between ​$6.25 and ​$6.75? Assume a normal distribution of wages.

The probability is _____.

Answer 1

Given:

= 6.50/hr, = 0.25

Find:

P(6.25 < X < 6.75)

Let X be the Workers wage.

Using Central Limit Theorem

P(6.25 < X < 6.75) = P(-1 < Z < 1)

P(6.25 < X < 6.75) = P(Z < 1) - P(Z < -1)

P(6.25 < X < 6.75) = 0.8413 - 0.1587 ............Using standard Normal table

P(6.25 < X < 6.75) = 0.6827

The probability is 0.6827