Question

Example 2 - Part 3 4. The annual salary for a certain job has a normal distribution with a mean of $54,000 and a standard deviation of a = $5000. What is the probability that the mean salary of a random selected sample has between $49,000 and $56, 150? a. Which picture (below) shows the requested area? Curve 3 Curve Image Curve 1 -40 -30 -10 To 2a Da 40 Curve 2 MacBook Air FT 80 F2 F4 F5 7 FB 2 % 5 3 4 & 7 8

Answer 1

Q4) a) We are given the distribution here as:

$X \sim N(\mu = 54000, \sigma = 5000)$

The probability required here is:

P(49000 < X < 56150)

Therefore the z scores here are computed as:
(49000 - 54000) / 5000 = -1
(56150 - 54000) / 5000 = 0.43

Therefore Curve 3 is the correct graph here.

b) The probability here is computed as:

= P(-1 < Z < 0.43)

= P(Z < 0.43) - P(Z < -1)

Getting it from the standard normal tables, we have here:
= 0.6664 - 0.1587

= 0.5077

Therefore 0.5077 is the required probability here.

c) Therefore there is a 50.77% chance that the value lies in the given range here ( as computed in the previous part here )