Question

Schools in Indonesia regularly measure the height and weight of primary school kids to compute their body mass index (BMI) in evaluating potential problems with their health.
Heights of primary school kids in Indonesia are normally distributed with a mean of 125cm and a standard deviation of 15cm.

a) Find the probability that a randomly selected kid would have a height more than 142cm. Display working.

b) Find the probability that the mean height for five randomly selected kids is less than 128cm. Display working.

c) Six kids are randomly selected. What is the probability that their mean height is between 120cm and 125cm? Display working.

d) Find the cut off height for the 3% shortest kids. Display working.

Answer 1

Using Z score=(X - mean) /standard deviation

Find these probability

A) P( X > 142) =0.12924

B) Using Z = (X-bar - mean )/ s.e.(x bar)

S.E.(x bar)= standard deviation/ square root of sample size

P( mean height <128 ) = 0.67256

C)

P( 120 < mean height < 125)= 0.29304

D)

P(X < Z ) =3% =0.03

Using normal distribution table find height

We get Height =96.785

Solution file is attached go through it

I think it was helpful

Thanks