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.
<u><em>Let </em></u><u><em> = sample mean weight of the pepperoni.</em></u>
The z score probability distribution for sample mean is given by;
Z = ~ N(0,1)
where, = population mean weight = 250 g
= 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( > 251 g)
P( > 251 g) = P(
>
) = P(Z > 2) = 1 - P(Z
2)
= 1 - 0.97725 = 0.02275
<em>The above probabilities is calculated by looking at the value of x = 2 in the z table which has an area of 0.97725.</em>
<em />
Hence, the probability that the mean weight of the pepperoni from the sample of 64 pizzas is greater than 251 g is 0.02275.