I NEED HELP WITH THESE PROBLEMS PLEASE SHOW STEPS ON HOW YOU

I NEED HELP WITH THESE PROBLEMS. PLEASE SHOW STEPS ON HOW YOU GOT THE ANSWER PLEASE

1. A widget manufacturer knows that their widget lengths are approximately Normally distributed with mean 12 inches and standard deviation 3.4 inches.

One widget is 9.8 inches long. That widget z-score is about:

Round to 4 decimal places.

2. A distribution of values is normal with a mean of 156.3 and a standard deviation of 76.9.

Find the probability that a randomly selected value is greater than 287.
P(X > 287) =

Solution

1)

z = ( X - Mean) / sigma

= (9.8 - 12 ) / 3.4

= -0.6471 Answer

2)

z= (287 - 156.3 ) / 76.9

= 1.6996

Therefore ,

P(X > 287) = 0.9554 Answer