#(1) the weight of a person selected randomly from a population of is normally d

Question

#(1) the weight of a person selected randomly from a population of is normally distributed with a mean of 160lbs and the standard deviation is 20lbs.

(i) Would it be expected that a big percentage of the population weighs more than 200lbs or less than 100lbs and explain why?

(ii) Compute and what of the percentage of the population weighs more than 200lbs but less than 100lbs.

(iii) What would be the median weight of this population?

# (2) there was IQ scores that can be modeled with a normal distribution with a mean of 100 and a standard deviation of 15.

(i) Write a formula for the density function of IQ scores.

(ii) Estimate a part of the population of IQs with 115and 120. Explain estimate.

(iii) Compute actual value of the estimate.

(iv) What range of scores that lie across on the other side of the mean represent the same fraction of the population. Please explain this probability in sentences.

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(#3)Does the normal distribution have a maximum with x=mu. What is the max value? Also please show that the normal distribution has points of inflection at x= mu + sigma and x=mu-sigma.

Explanation / Answer

#1)

(i) No . because 200 and 100 are far away from mean

(ii)P(X>200) = 0.0227 ==> 2.27% and P(X<100) = 0.00135 ==> 0.135%

(iii) median = 160lbs

#2)

(i) f(x) = (e^- ((x-160)^2 /(2*400) ) /(20*sqrt(2pi) )

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