Question

The weight of male babies less than 2 months old in the United States is normally distributed with mean 12.3 pounds and standard deviation 3.8 pounds.

(a) Find the 84 th percentile of the baby weights.

(b) Find the 11 th percentile of the baby weights.

(c) Find the third quartile of the baby weights.

Use the TI-84 Plus calculator and round the answers to at least two decimal places.

Answer 1

We have given the normal distribution

mean = μ = 12.3

standard deviation = σ = 3.8

# a part

We have 84th percentile means we have given the left side area as 84 %

We convert the left side area into decimal =0.84

Ti-84 calculator path

Press " 2nd "

Press " VARS "

select "invNorm "

Area = 0.84

μ = 12.3

σ = 3.8

i.e invNorm(0.84 , 12.3 , 3.8)

Press" Enter "

We get 16.07893998

We round to 2 decimal place

16.08

Answer for # a :

84 th percentile of the baby weights = 16.08 pounds

# b part

We have 11th percentile means we have given the left side area as 11 %

We convert the left side area into decimal =0.11

Ti-84 calculator path

Press " 2nd "

Press " VARS "

select "invNorm "

Area = 0.11

μ = 12.3

σ = 3.8

i.e invNorm(0.11, 12.3 , 3.8)

Press" Enter "

We get 7.639193142

We round to 2 decimal place

7.64

Answer for # b :

11 th percentile of the baby weights = 7.64 pounds

# C part

Area to the left side of the third quartile 75%

We convert that left side area in to decimal = 0.75

Ti-84 calculator path

Press " 2nd "

Press " VARS "

select "invNorm "

Area = 0.75

μ = 12.3

σ = 3.8

i.e invNorm(0.75, 12.3 , 3.8)

Press" Enter "

We get 14.86306105

We round to 2 decimal place

14.86

Answer for # c :

third quartile of the baby weights = 14.86 pounds

I hope this will help you :)