Question

The heights of 10 year old children has a normal probability distribution with mean of 54.6 inches and standard deviation of 5.7 inches. What is the approximate probability that a randomly selected 10-year old child will be more than 51.75 inches tall? Group of answer choices 0.69 0.31 0.62 0.67 0.93

Answer 1

a) 0.69

The probability that a randomly selected 10-year old child will be more than 51.75 inches tall

P(X>51.75 ) = 0.6915

Explanation:

Step(i):-

Given mean of the Population = 54.6 inches

Given standard deviation of the Population = 5.7 inches

Let 'X' be the random variable of normal distribution

Let 'X' = 51.75 inches

`Z = (x-mean)/(S.D) = (51.75-54.6)/(5.7) = -0.5`

Step(ii):-

The probability that a randomly selected 10-year old child will be more than 51.75 inches tall

P(X>51.75 ) = P(Z>-0.5)

= 1 - P( Z < -0.5)

= 1 - (0.5 - A(-0.5))

= 1 -0.5 + A(-0.5)

= 0.5 + A(0.5) (∵A(-0.5)= A(0.5)

= 0.5 +0.1915

= 0.6915

Conclusion:-

The probability that a randomly selected 10-year old child will be more than 51.75 inches tall

P(X>51.75 ) = 0.6915