Question

Can someone help me with this stats problem???

Suppose that the diameters of golf balls manufactured by a certain company are normally distributed with mean of 1.94 inches and standard deviation of 0.03 inch. A golf ball will be considered defective if its diameter is less than 1.89 inches or greater than 1.99 inches. What is the probability of defective balls manufactured by the company?

Answer 1

mean: mu = 1.94
standard deviation: sigma = 0.03

for the raw score x = 1.89, the z-score is

z = (x-mu)/sigma
z = (1.89-1.94)/0.03
z = -1.67

Answer 2

If the raw score is x = 1.99, then what is the z-score?

Answer 3

@jim_thompson5910 is is 1.6667?

Answer 4

yes it is

Answer 5

I'm going to round it to 1.67 so we can use this table here

https://www.stat.tamu.edu/~lzhou/stat302/standardnormaltable.pdf

Answer 6

according to that table

P(Z < -1.67) = 0.04746

P(Z < 1.67) = 0.95254

do you see how I'm getting those values from the table?

Answer 7

@jim_thompson5910 Yes! looking at -1.6 and +1.67 at 0.07

Answer 8

good

Answer 9

we have this normal distribution