Question

A soft-drink machine at a steak house is regulated so that the amount of drink dispensed is approximately normally distributed with a mean of 210 milliliters and a standard deviation of 12 milliliters. The machine is checked periodically by taking a sample of 9 drinks and computing the average content. If x falls in the interval 204<x<216, the machine is thought to be operating satisfactorily; otherwise, the owner concludes that u # 210 milliliters. Complete parts (a) and (b) below. Click here to view page 1 of the standard normal distribution table. Click here to view page 2 of the standard normal distribution table. (a) Find the probability of committing a type I error when u = 210 milliliters. The probability is . (Round to four decimal places as needed.) (b) Find the probability of committing a type II error when u = 198 milliliters. The probability is . (Round to four decimal places as needed.)

Answer 1

a)

for normal distribution z score =(X-μ)/σx
mean μ=	210
standard deviation σ=	12.00

sample size       =n=

9

std error=σx̅=σ/√n=

4.000

type I error =1-P(204<X<216)=1-P((204-210)/4)<Z<(216-210)/4)=1-P(-1.5<Z<1.5)=1-(0.9332-0.0668)=0.1336

b)

type II error =P(204<X<216)=P((204-198)/4)<Z<(216-198)/4)=P(1.5<Z<4.5)=1-0.9332=0.0668