Answer to Question #167512 in Statistics and Probability for rururururu

Question #167512

The weights of a normally distributed group of adults participating in a fitness test has an average of 60kg and a standard deviation of 8kg.

a. What is the probability that an adult’s weight is in between 55-65kg?

b. What raw score divides the group such that 55% is above it?


1
Expert's answer
2021-03-01T07:15:19-0500

Given, Average weight "\\mu=60kg"

Standard deviation "\\sigma=8kg"


(a) Probability that adult's weight lies in 55-65 kg =

"P(55<X<65)=P(\\dfrac{55-60}{8}<z<\\dfrac{65-60}{8})"


"=P(-0.625<z<0.625)"


"=1-2P(z>0.625)"


"=1-2(0.7324)=1-1.4648=0.5352"


(b) As the 55% groups above it

the z value at 0.55 is 0.7088

Then raw score

"X=\\mu+z\\times \\sigma"

"=60+0.7088(8)=60+5.6704=65.6704."


Hence The raw score is 65.6704.


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