1. A survey shows that the amount paid for a new Honda Civic has a mean of $1820

Question

1. A survey shows that the amount paid for a new Honda Civic has a mean of $18200 with a standard deviation of $950. Find the probability that:

a) The amount paid for a new Honda Civic is greater than $17500

b) The mean amount paid for a random sample of 8 new Honda Civics is greater than $17500

           c) The amount paid for a new Honda Civic is between $18000 and $19000

           d) The mean amount paid for a random sample of 8 new Honda Civics is between $18000 and $19000

2. The operating life of a lawn mower has a mean of 9.2 years with a standard deviation of 2.8 years. If a manufacturer will replace 0.50% of lawn mowers for a major malfunction, what is the maximum time that the warranty will cover?

Explanation / Answer

1) a)
P(x>17500) = P( z> (17500-18200)/950)=0.7694

b)stdev of mean = stdev/sqrt(n)= 950/sqrt(8)

P(x>17500) = P( z> (17500-18200)/(950/sqrt(8)))=0.9814

c) P(18000<x<19000) = P( z< (19000-18200)/950)-P( z< (18000-18200)/950)=0.8001-0.4166= 0.3835

d) stdev of mean = stdev/sqrt(n)= 950/sqrt(8)
P(18000<x<19000) = P( z< (19000-18200)/(950/sqrt(8))))-P( z< (18000-18200)/(950/sqrt(8))))=0.9914-0.2758=0.7156

2) P(z<c) = 0.005
z = -2.576

so max time = 9.2-2.576*2.8=1.9872 years

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