Question

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

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

(ii) Computeand what of the percentage of the population weighs more than200lbs but less than 100lbs.

(iii) Whatwould be the median weight of this population?

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

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

(ii) Estimatea part of the population of IQs with 115and 120. Explainestimate.

(iii) Computeactual value of the estimate.

(iv) Whatrange of scores that lie across on the other side of the meanrepresent the same fraction of the population. Please explain thisprobability in sentences.

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