Answer to Question #281037 in Statistics and Probability for aparajita mishra

Question

Suppose that a doorway being constructed is to be used by a class of people

whose heights are normally distributed with mean 70 cms. and standard deviation 3

cms. How long may the doorway be without causing more than 25% of the people

to bump their heads? If the height of the doorway is fixed at 76 cms., how many

persons out of 5000 are expected to bump their heads? (Given Φ(2) = 0.4762).

Answer 1

Solution:

Given, mean = 70 cm.

standard deviation = 3 cm.

for no more than 25% of the people to bump their heads, the height of the door needs to be at least 72.023 cm.

Next, if the height of the doorway is fixed at 76 cm, the proportion of people who will bump their heads becomes 0.0228.

.0228 x 5000 = 114.