Question

4. SeeClear Windows makes windows for use in homes and commercial buildings. The standards for glass thickness call for the glass to average 0.375 inches with a standard deviation equal to 0.050 inches.
a. What is the population mean thickness of the windows that meet the standard?

b. What is the population standard deviation of the windows that meet the standard?

c. What is the probability that a random glass X will be thicker than 0.392 inches if the windows meet the standard?(in decimal format, round to 4 decimal digits, e.g. 0.1111)

d. Suppose we randomly select 64 pieces of windows, what is the mean thickness of all possible sample means?

e. Suppose we randomly select 64 pieces of windows, what is the standard deviation of all possible sample means (standard error)? (in decimal format, round to 3 decimal digits, e.g. 0.111)

f. Suppose we randomly select 64 pieces of windows, what is the probability that one sample mean X_bar will be thicker than 0.392 inches if the windows meet the standards? (in decimal format, round to 4 decimal digits, e.g. 0.1111)

Answer 1

a.

population mean thickness , = 0.375 inches

b.

population standard deviation, = 0.050 inches

c.

probability that a random glass X will be thicker than 0.392 inches = P(X > 0.392)

= P[Z > (0.392 - 0.375) / 0.050]

= P[Z > 0.34]

= 0.3669

d.

By Central limit theorem, mean thickness of all possible sample means is population mean thickness , = 0.375 inches

e.

Standard deviation of all possible sample means (standard error) = / = 0.050 / = 0.006

Probability that one sample mean X_bar will be thicker than 0.392 inches = P( > 0.392)

= P[Z > (0.392 - 0.375) / 0.006]

= P[Z > 2.83]

= 0.0023