The serum cholesterol levels of a certain population of boys follow a normal dis

Question

The serum cholesterol levels of a certain population of boys follow a normal distribution with a mean of 170 mg/dl and a standard deviation of 30 mg/dI (a) Find the probability that a randomly chosen boy has a serum cholesterol level of 155 mg/dl or less (b) Find the percentage of boys with values between 125 mg/dl and 215 mg/dl (c) Find the probability that the mean serum cholesterol level of a random sample of 25 boys is below 182 mg/dl. (d) Determine the probability that the mean serum cholesterol level of a random sample of 100 boys is below 164 mg/dl.

Explanation / Answer

Here it is given that mean is 170 and sd=30

a. We need to find P(x<=155)

As it given normal distribution. We will convert x to z

P(z<=155-170/30)=P(z<=-0.5)=0.3085

b. Here we need to find P(125<x<215)=P(125-170/30<z<215-170/30)=P(-1.5<z<1.5)=0.8664

c. P(xbar>=182)

As per central limit theorem mean of xbar =170 and sd=30/5=6

So P(z<=182-170/6)=P(z<=2)=0.9772

d. P(x<164)=P(z<164-170/6)=P(z<-1)=0.1587

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