1. The U.S. Bureau of Labor Statistics reports that the average annual expenditu

Question

1. The U.S. Bureau of Labor Statistics reports that the average annual expenditure on food and drink for all families is $5,700 (Money, December 2003). Assume that annual expenditure on food and drink is normally distributed and that the standard deviation is $1,500. (50 points)

What is the range of expenditures of the 24.2% of families with the lowest annual spending on food and drink?

Assume total number of families is 500,000. How many families spend more than $7000 annually on food and drink?

Explanation / Answer

here for 24.2 percentile z score =-0.70

hence  expenditures of the 24.2% of families with the lowest annual spending on food and drink

=mean+z*std deviation =5700-0.70*1500=$4650

P(X>7000)=1-P(X<7000)=1-P(Z<(7000-5700)/1500)=1-P(Z<0.8667)=1-0.8069=0.1931

hence families spend more than $7000 annually on food and drink =np=500000*0.1931~96550

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