Monogram Masters advertises on its website that 92% of customer orders are received within five working days. They performed an audit from a random sample of 200 of the 3,000 orders that month and it shows 175 orders were received on time. Part A: Can we use a normal approximation? Explain. (5 points)

Part B: If Monogram Masters customers really receive 92% of its orders within five working days, what is the probability that the proportion in the random sample of 200 orders is the same as the proportion found in the audit sample or less? (5 points)

Step-by-step explanation:

yes

0.0094

Step-by-step explanation:

p = 0.92, n = 200

np = 184 > 10

n(1 − p) = 16 > 10

Therefore, normal approximation can be used.

μ = p = 0.92

σ = √(p (1 − p) / n)

σ = √(0.92 × 0.08 / 200)

σ = 0.0192

x = 175/200 = 0.875

z = (x − μ) / σ

z = (0.875 − 0.92) / 0.0192

z = -2.35

P(z < -2.35) = 0.0094

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.