Question

The Chemco Company manufactures car tires that last distances

8. The Chemco Company manufactures car tires that last distances having a normal distribution with a mean of 35,000 miles and a standard deviation of 4275 miles. If the manufacturer wants to guarantee the tires so that only 3% will be replaced because of failure before the guaranteed number of miles, for how many miles should the tires be guaranteed? 9. A random sample of 50 cars in the drive-thru of a popular fast food restaurant revealed an average bill of $18.21 per car. The population standard deviation is $5.92. Estimate the mean bill for all cars from the drive-thru with 98% confidence.

Answer 1

8. Solution :

Given that,  

mean = $\mu$ = 35000

standard deviation = $\sigma$ = 4275

Using standard normal table,

P(Z < z) =3%

P(Z < -1.88) = 0.03

z = -1.88

Using z-score formula,

x = z * $\sigma$ + $\mu$

x = -1.88 * 4275 + 35000 = 26963

26963 should the tires be guaranteed