A tire manufacturer is measuring the margin of error in the thickness of their tires to make sure it is within safety limits. Overall, the tires' thickness is normally distributed with a mean of 0.45 inches and a standard deviation of 0.05 inches. What thickness separates the lowest 5% of the means from the highest 95% in a sample size of 65 tires

Z = -1.65

Step-by-step explanation:

The main objective is to compute the data for the Z value and determine the of the sample distribution

Given that;

the tires' thickness is normally distributed  with a mean μ = 0.45 in

standard deviation σ = 0.05 in

sample size  =  65 tires

Also; we are being told that the  thickness separates the lowest 5% of the means from the highest 95%

∴

P(Z < Z) =0.05

From the Z- table

P(Z < -1.645) = 0.05

Z = -1.65

Similarly;

Let consider  to be the sample mean;

Then:

mean

standard deviation

= 0.00620174

By applying the Z-score formula:

x =  μ + ( Z × σ )

step-by-step explanation: