Determine if the outcome is unusual. Consider as unusual any result that differs from the mean by more than 2 standard
deviations. That is, unusual values are either less than $\mu - 2 \sigma$ or greater than $\mu + 2 \sigma$
-The Acme Candy Company claims that 60% of the jawbreakers it produces weigh more than .4 ounces. Suppose that 800 jawbreakers are selected at random from the production lines. Would it be unusual for this sample of
800 to contain 494 jawbreakers that weigh more than .4 ounces?
A) Yes
B) No

Question

Quizplus · Accepted Answer

The mean (μ) of a binomial distribution is given by n*p, where n is the sample size and p is the probability of success. In this case, the mean is:

μ = 800*0.6 = 480

The standard deviation (σ) of a binomial distribution is given by sqrt(n*p*(1-p)). In this case, the standard deviation is:

σ = sqrt(800*0.6*0.4) = 15.49

To determine if 494 jawbreakers weighing more than .4 ounces is unusual, we need to calculate how many standard deviations it is away from the mean:

z = (494 - 480) / 15.49 = 0.904

Since 0.904 is less than 2, it is not considered an unusual outcome. Therefore, the answer is B, No.

Determine If the Outcome Is Unusual μ−2σ\mu - 2 \sigmaμ−2σ Or Greater Than

Determine If the Outcome Is Unusual $\mu - 2 \sigma$ Or Greater Than