Question

The weight of extra-large egg has a Normal distribution with a mean of 3 oz and a standard deviation of 0.1 oz. In sampling distribution, what is the most feasible probability that an egg in a carton of a dozen eggs weighs more than 3.5 oz

Answer 1

Answer:

Probability = 0.4443

Step-by-step explanation:

The provided information is:

Consider X be the weight of extra-large egg that is normally distributed with mean $\mu=3 \,oz$ and standard deviation $\sigma = 0.1 \,oz$

Also, sample size n = 12.

Thus, the probability that an egg in a carton of a dozen eggs weights more than 3.5 oz is:

$\begin{aligned}P( X > 3.5) &= P(Z >\frac{3.5-3}{\frac{0.1}{\sqrt{12}}})\\&=P(Z>0.14)\\&=1-P(Z\leq0.14)\\&=1-0.557\\&=0.4443\end{aligned}$