Having the most trouble with D and percentiles at the moment

(Having the most trouble with D) and percentiles at the moment)

The waste circumfrance of males 20 to 29 years old is approximately normally distributed, with mean 87.5 cm and standard deviation 10.2cm

a) Use normal model to see if the proportion of 20 to 29 yr ol males who waist circumfraence is less than 100cm.

b) What is the probaility tha a randomly selected 20 to 29 yr ol male has a waist circumference between 80 and 100cm?

c)determine the waist circumfrences that represetn the middle 90% of all waist circumfreerences.

d)Determine the waist circumference that is at the 10th cercentile. .

Mean =87.5 and sigma =10.2

a) P(X<100) = P(Z<-12.5/10.2) =P(Z<-1.225)

=0.5-0.3907

= 0.1093

b) P(80<x<100) = P(-0.74<z<-1.225) =0.3907- 0.2704

= 0.1203

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c) Middle 90% = 87.5-10.2(1.64)<x<87.5+10.2(1.64)

i.e.(70.772 ,104.228)

d) 10th percentile =87.5 -1.28(10.2) = 74.444