Question

An amount of purchase of a customer in a mall of a city follows normal distribution with mean₹ 800 and standard deviation ₹ 200. If a customer is selected at random, then find the probabilities for the following events:
(1) Amount of purchase made by him is in between ₹ 850 to ₹ 1200.
(2) Amount of purchase made by him is in between ₹ 600 to ₹ 750.

Answer 1

Here, µ = 800; σ = 200
X = Amount of purchase (₹)

(1) Amount of purchase is between ₹ 850 to ₹ 1200:

P[850 ≤ X ≤ 1200] = ?
For x₁ = 850,

P[850 ≤ X ≤ 1200] = P[0.25 ≤ Z ≤ 2]
= P[0 ≤ Z ≤ 2] – P[0 ≤ Z ≤ 0.25]
= 0.4772 – 0.0987
= 0.3785

Hence, the probability that the amount of purchase is between ₹ 850 to ₹ 1200, obtained is 0.3785.

(2) Amount of purchase is between ? 600 and f 750:

P[600 ≤ X ≤ 750] = ?
For x₁ = 600,

P[600 ≤ X ≤ 750] = P[- 1≤ Z ≤ – 0.25]
= P[- 1 ≤ Z ≤ 0] – P[- 0.25 ≤ Z ≤ 0]
= P[0 ≤ Z ≤ 1] – P[0 ≤ Z ≤ 0.25]
= 0.3413 – 0.0987
= 0.2426