Answer:
0.00621
Explanation:
To solve for this question: we would be making use of the z score formula.
z = (x - μ)/σ
where
x is the raw score
μ is the population mean
σ is the population standard deviation
Step 1
Find the Standard Error
From the above question, we are given number of samples, hence, the standard deviation we would use for our z score is Standard error.
Standard error = Standard deviation/√n
Where n = number of samples = 25
Standard deviation = 4
Standard error = 4/√25
= 4/5
= 0.8
Step 2
Calculate the z score
Since we are given number of samples in the question,
z score = z = (x - μ)/σ
where
x is the raw score = 14
μ is the population mean = 12
σ is the standard error = 0.8
z score = 14 - 12/0.8
z score = 2.5
Step 3
We find the Probability.
The probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is calculated as:
We find the Probability of the Z score 2.5 using a Z table.
P(z = 2.5) = P(x ≤ 14) = 0.99379
P(x > 14) = 1 - P(x<14)
= 1 - 0.99379
= 0.0062097
Approximately ≈ 0.00621
Therefore, the probability that a randomly selected sample of 25 students will consume on average more than 14 pizzas per month is
0.00621