Question

The distribution of weights of a large group of high school students is normally distributed with mean 55 kg and standard deviation 5 kg. Which of the following is true?

a.about 2.5% will be below 40 kg

b.about 16% of the students will be over 65 kg

c.half of them can be expected to weigh less than 55kg

d.about 2.5% will weigh more than 60 kg

Answer 1

Solution:

We are given,

Mean = = 55

Standard deviation = = 5

Here we need to check all options.

a) We need to check P( x < 40 ) = ______ ?

Using excel , =NORMDIST(40,55,4,TRUE)

P( x < 40 ) = 0.0013 = 1.3%

and we are given that about 2.5% will be below 40 kg. Which is false statement.

b) We need to check P( x > 65 )= _______ ?

Using excel , =1-NORMDIST(65,55,4,TRUE)

P( x > 65 )= 0.0227 = 2.27%

and we are given that about 16% of the students will be over 65 kg. Which is false statement

c) We need to check P( x < 55 )= ________ ?

Using excel , =NORMDIST(55,55,4,TRUE)

P( x < 55 )= 0.5 = 50%

and we are given that  half(50%) of them can be expected to weigh less than 55 kg. Which is correct.

d) We need to check P( x > 60 )= ________ ?

Using excel , =2-NORMDIST(60,55,4,TRUE)

P( x > 60 )= 0.9516 = 95%

and we are given that about 2.5% will weigh more than 60 kg. Which is false statement

Hence option C is correct

Done