Question

A factory makes components used in jet engines, including reinforced steel washers. The washers are required to have a very precise thickness. The thickness of the washers follow a normal distribution with mean 1. 59 millimeters and standard deviation 0. 042 millimeters. A technician randomly samples washers and calculates the mean of their thicknesses, which is. What is the probability that ?.

Answer 1

The probability that $\bar{x}$ < 1.57 for the given mean, standard deviation , and samples is equal to 0.0162.

As given in the question,

Normal distribution with mean 'μ' = 1.59 millimeters

Standard deviation 'σ' = 0.042 millimeters

Sample size 'n' = 20

standard error = σ /√n

                        = 0.042 / √20

                        = 0.00933

Probability that $\bar{x}$ < 1.57  is

X = 1.57

s = 0.0093

P( X < 1.57)

= P[ (X -μ)/s < ( 1.57 - 1.59)/ 0.0093]

= P ( z < -2.14 )

Using z - table p value is

= 0.01617

= 0.0162

Therefore, the probability for the $\bar{x}$ < 1.57  is equal to 0.0162.

The complete question is :

A factory makes components used in jet engines, including reinforced steel washers. the washers are required to have a very precise thickness. the thickness of the washers follow a normal distribution with mean 1.59 millimeters and standard deviation 0.042 millimeters. a technician randomly samples n = 20 washers and calculates the mean of their thicknesses, which is x¯. what is the probability that x¯<1.57?

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