Question

Please assist to detail the find by step for the following:

The average height of a female adult in Australia is 175.6cm, with variance 25cm,  find the probability that a randomly selected man measures between 178 and 184 centimetres.  

Assuming a normal distribution

Answer 1

given data .

here we have to faindout Z values for 178 cm & 184cm

= 0.48

= 1.68

Form normal distribution table

P(Z) we will findout.

P(0.48) =0.6844

P(1.68) =0.9535

probability for getting man between 178 & 184 is

P(178 < Xi < 184) = P(Z(184)) -P(z(178))

= P(1.68) -P(0.48)

= 0.9535 -0.6844

= 0.2691

Probability for getting man between 178 & 184 is 0.2691 ie,. 26.91%