The annual ground coffee expenditures for households are approximately normally

Question

The annual ground coffee expenditures for households are approximately normally distributed with a mean of $45 76 and a standard deviation of $10.00 a-Find the probability that a household spent krss than $25 00 b. Find the probability that a household spent more than $55 00 c. What proportion ot the households spont betweon $30.00 and $40 00 d-97 5% of the households spent less than what amount? a. The probability that a household spent less than $2500 ts (Round to lour decimal places as needed) b. Tho probability that a housohold spont more than $55 00 (Round to four decimal places as needed) c. The proportion of the housoholds that spent botweon $30 00 and $40 00 s (Round to tour decimal placos as needed) d, 97 5% of the households spent less than (Round to the nearest cent as needed)

Explanation / Answer

Ans:

a)

z=(25-45.76)/10=-2.076

P(z<-2.076)=0.0189

b)

z=(55-45.76)/10=0.924

P(z>0.924)=0.1777

c)

z(30)=(30-45.76)/10=-1.576

z(40)=(40-45.76)/10=-0.576

P(-1.576<z<-0.576)=P(z<-0.576)-P(z<-1.576)

=0.2823-0.0575=0.2248

d)

P(Z<=z)=0.975

z=normsinv(0.975)=1.96

x=45.76+1.96*10=65.36

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