Question 903026: The life time of a heavy lift machine is normally distributed, with mean of 7.2 years and standard deviation of 2.3 years.
a.If the manufacturer guarantees the machine for 3 years, what is the chance that a randomly chosen machine will wear out before the guarantee has expired?
b.If the manufacturer is willing to replace only 2% of all machines due to early failure, how should he change the guarantee?
c.If we choose a sample of 20 machines, what is the chance that the average life time for the sample is less than 8 years?
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
TI syntax is normalcdf(smaller, larger, µ, σ).
Note: The -100 is used as the smaller value to be at least 5 standard deviations from the mean.
a. P(x < 3) = normalcdf(-100, 3, 7.2, 2.3)
0r P(z < -1.8261)
b. z = invNorm(.98)=( X-7.2)/2.3
2.3invNorm(.98) + 7.2 = X, number of years needed for the guarantee
c. P(x < 8) = P(z < .8/(2.3/sqrt(20)) )
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