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.

g. Suppose we randomly select 64 pieces of windows, what is the probability that the sample mean will be thinner than 0.37 inches? (in decimal format, round to 4 decimal digits, e.g. 0.1111)

Answer 1

Given

= 0.375

=0.050

Also given n=64

Now calculate p(x < 0.37)

P(x < 0.37) = 0.5 - p(0 < z < x_bar -/(/n))

= 0.5 - p(0 < z < 0.37-0.375/(0.050/64))

= 0.5 - p(0 < z < -0.80)

= 0.5 - 0.2881

P(x <0.37) = 0.2119

Therefore the probability that the sample mean will be thinner than 0.37 inches is 0.2119.