A factory produces plate glass with a mean thickness of 4 mm and a standard deviation of 1.1 mm. A simple random sample of 100 sheets of glass is to be measured, and the mean thickness of the 100 sheets is to be computed. What is the probability that the average thickness of the 100 sheets is less than 3.74 mm

Using the normal distribution and the central limit theorem, it is found that there is a 0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

In a normal distribution with mean and standard deviation , the z-score of a measure X is given by:

In this problem:

The probability is the p-value of Z when X = 3.74, then:

By the Central Limit Theorem

has a p-value of 0.0091.

0.0091 = 0.91% probability that the average thickness of the 100 sheets is less than 3.74 mm.

A similar problem is given at link

0.0090483

Approximately = 0.00905

Step-by-step explanation:

z = (x - μ)/σ, where

x is the raw score = 3.74

μ is the sample mean = population mean = 4 mm

σ is the sample standard deviation

This is calculated as:

= Population standard deviation/√n

Where n = number of samples = 100

σ = 1.1/√100

σ = 1.1/10 = 0.11

z = (3.74 - 4) / 0.11

z = -2.36364

Using the z score table to determine the probability,

The probability that the average thickness of the 100 sheets is less than 3.74 mm

P(x<3.74) = 0.0090483

Approximately = 0.00905

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,