A bank's loan officer rates applicants for credit. The rating

Gregory Jones

Gregory Jones

Answered question

2021-12-19

A bank's loan officer rates applicants for credit. The rating are normally distributed with a mean of 705 and a standard deviation of 32. If 50 different applicants are randomly selected, find the probability that their mean is above 700.

Answer & Explanation

Linda Birchfield

Linda Birchfield

Beginner2021-12-20Added 39 answers

Step 1
From the given information,
Mean = 705
Standard deviation = 32
Sample size = 50
Step 2
The probability that their mean is above 700 is,
P(x>700)=P(xμσn>700μσn)
=P(Z>700μσn)
=P(Z>7007053250)
=P(Z>-1.10)
=1P(Z1.10)
=1-0.1357 (Using standard normal table)
=0.8643
Jonathan Burroughs

Jonathan Burroughs

Beginner2021-12-21Added 37 answers

μ=705,σ=32,m=50
XN(μ,(σn)2)
P(X>700)=1P(X700)
=1P(Z7007053250)
=1ϕ(11)=0.8643

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