Answer:
The probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.
Step-by-step explanation:
We are given that the owner of the pizza chain wants to monitor the total weight of pepperoni. Suppose that for pizzas in this population, the weights have a mean of 250 g and a standard deviation of 4 g.
Management takes a random sample of 64 of these pizzas.
Let [tex]\bar X[/tex] = sample mean weight of the pepperoni.
The z score probability distribution for sample mean is given by;
Z = [tex]\frac{X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] ~ N(0,1)
where, [tex]\mu[/tex] = population mean weight = 250 g
[tex]\sigma[/tex] = standard deviation = 4 g
n = sample of pizzas = 64
Now, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is given by = P([tex]\bar X[/tex] > 251 g)
P([tex]\bar X[/tex] > 251 g) = P( [tex]\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }[/tex] > [tex]\frac{251-250}{\frac{4}{\sqrt{64} } }[/tex] ) = P(Z > 2) = 1 - P(Z [tex]\leq[/tex] 2)
= 1 - 0.97725 = 0.02275
The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.
Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.
