Question

in a countyof united states of heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.6 inches and standard deviation of 2.6 inches.

A) What is the probabilty that a randomly chosen child has a height of less than 60.8 inches?______round three decimal places

B) What is the probability that a randomly chosen child has a height of more than 48.7 inches?_______round three decimal places.

Answer 1

Given,

$\mu$ = 55.6, $\sigma$ = 2.6

We convert this to standard normal as

P( X < x) = P( Z < x - $\mu$ / $\sigma$ )

A)

P( X < 60.8) = P( Z < 60.8 - 55.6 / 2.6)

= P( Z < 2)

= 0.977

B)

P( X > 48.7) = P( Z > 48.7 - 55.6 / 2.6)

= P( Z > -2.6538)

= P( Z < 2.6538)

= 0.996