Answer:
0.964 is the probability that their mean shoulder breadth is less than 18.5 inch.
Step-by-step explanation:
Given:
Mean, μ = 18.2 inch
Standard Deviation, σ = 1.0 inch
n = 36
We are given that the distribution of shoulder breadths is a bell shaped distribution that is a normal distribution.
Formula:
a) P( mean shoulder breadth is less than 18.5 inch)
P(x < 18.5)
Calculation the value from standard normal z table, we have,
![P(x < 18.5) =0.964= 96.4\%](https://tex.z-dn.net/?f=P%28x%20%3C%2018.5%29%20%3D0.964%3D%2096.4%5C%25)
Thus, 0.964 is the probability that their mean shoulder breadth is less than 18.5 inch.
Yes, the result suggest that money can be saved by making smaller manholes with a diameter of 18.5 inch since 96.4% of the man holes have their mean shoulder breadth less than 18.5 inch.