A bank's loan officer rates applicants for credit. The ratings are normally distributed with a mean of 200 and a standard deviation of 50. If an applicant is randomly selec…

Question

asked Oct 25, 2021 179k views

1 Answer

Thomas Owens · Answer 1 · 2021-10-31T10:18:18+0000

Answer:

$P(170<X<220)=P((170-\mu)/(\sigma)<(X-\mu)/(\sigma)<(220-\mu)/(\sigma))=P((170-200)/(50)<Z<(220-200)/(50))=P(-0.6<z<0.4)$

And we can find the probability with this difference:

P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)

And using the normal standard table or excel we got:

P(-0.6<z<0.4)=P(z<0.4)-P(z<-0.6)=0.6552-0.2742=0.3811

And the best answer would be:

0.3811

Explanation:

Let X the random variable that represent the ratings of a population, and for this case we know the distribution for X is given by:

$X \sim N(200,50)$

Where
$\mu=200$ and
$\sigma=50$

We are interested on this probability

P(170<X<220)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=(x-\mu)/(\sigma)$