Question

On average 4 customers enter a store every 10 minutes.

I. The probability of 30 clients entering in one hour is 0.0363.

II. The probability that between 2 and 5 (inclusive) customers enter the store in a period of 10 minutes is 0.6936

a. Only I is correct.

b. Only II is correct.

c. Both are correct.

d. None is correct.

Answer 1

$P(X = x)=\frac{e^{-\mu} * \mu ^x}{x!}$

I) mean = 4 per 10 minutes = 4 * 6 = 24 per 1 hour

P(X = 30) = e^{​​​​​​-24} * 24³⁰ / 30! = 0.0363

Ii) mean = 4

P(2 < X < 5) = P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

= e^-4​ * 4² / 2! + e^-4 * 4³ / 3! + e^-4 * 4⁴ / 4! + e^-4 * 4⁵ / 5!

= 0.6936

Option-C) Both are correct