Question

According to Money magazine, Maryland had the highest median annual household income of any state in 2018 at $75,847.† Assume that annual household income in Maryland follows a normal distribution with a median of $75,847 and standard deviation of $33,800.

(a)

What is the probability that a household in Maryland has an annual income of $110,000 or more? (Round your answer to four decimal places.)

(b)

What is the probability that a household in Maryland has an annual income of $50,000 or less? (Round your answer to four decimal places.)

(c)

What is the probability that a household in Maryland has an annual income between $40,000 and $70,000? (Round your answer to four decimal places.)

(d)

What is the annual income (in $) of a household in the ninety-first percentile of annual household income in Maryland? (Round your answer to the nearest cent.)

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	75847
std deviation   =σ=	33800.000

a)

probability =

P(X>110000)

=

P(Z>1.01)=

1-P(Z<1.01)=

1-0.8438=

0.1562

b)

probability =

P(X<50000)

=

P(Z<-0.76)=

0.2236

c)

probability =

P(40000<X<70000)

=

P(-1.06<Z<-0.17)=

0.4325-0.1446=

0.2879

d)

for 99th percentile critical value of z=		2.33
therefore corresponding value=mean+z*std deviation=			154601.00