Question

The heights of women in New Zealand are normally distributed, with a mean of 165 centimetres and a standard deviation of 10 centimetres. What is the probability that a randomly selected woman in New Zealand is shorter than 162 centimetres?

Group of answer choices

0.9452.

0.4452.

0.3554.

0.3821.

Answer 1

Here, we have heights of women in New Zealand as the variable and let us denote it by x.

As per question we have µ=165

                                  and σ= 10

Here, we have to find p(x≤162)

To find out probability from normal distribution we need to convert x values into z values

The z values can be obtained as

For x=162,

That means we have to find p(z≤ -0.3)

From standard normal table we can find the probability of z≤-0.3

p(z≤-0.3) = 1- p(z≤0.3) = 1- 0.6179114 = 0.3820886 ≈ 0.3821

Hence the probability that the heights of women in New Zealand is shorter than 162 centimetres is 0.3821

The correct option is D.