Please show how to solve step by step. thanks A. A study of homeowners in the 5t

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Please show how to solve step by step. thanks

A. A study of homeowners in the 5th congressional district in Maryland found that their annual household incomes are normally distributed with a mean of $41,182 and a standard deviation of $11,990 (based on data from Nielsen Media Research). What percentage of household incomes are between $25,000 and $40,000? o 53.93% 62.5% ? 28.23% 37.22% B. An airline knows from experience that the distribution of the number of suitcases that get lost each week on a certain route is approximately normal with 15.5 and ?-36. What is the probability that during a given week the airline will lose less than 20 suitcases? 0.8944 0.1056 ? 0.3944 0.4040

Explanation / Answer

Solution A:

X follows normal distribution with mean=41182 sd=11990

P(25000<X<40000)

z=x-mean/sd

(25000-41182/)11990<Z<(40000-41182)/11990

P(-1.35<Z<-0.1)

P(Z<-0.1)-P(Z<-1.35)

=(1-P(Z<0.1)-(1-P(Z<1.35))

=(1-0.5398)-(1-0.9115)

=0.3717

=0.3717*100

=37.17%

ANSWER:37.17%

SolutionB:

mean=15.5

sd=3.6

P(X<20)

P(Z<20-15.5/3.6)

=P(Z<1.25)

From standard normal tables

=0.8944

ANSWER:0.8944

option A

37.22%

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