Question

X∼N(2.2,1.44). Find the P(X<3.4)

A. 8413
B. 5
C 1.00
D. .1587
E. 2097

Answer 1

To find the probability P(X < 3.4) when X follows a normal distribution with a mean of 2.2 and a variance of 1.44, we can use the standard normal distribution.

Step 1: Standardize the value of 3.4 using the formula z = (x - μ) / σ, where x is the given value, μ is the mean, and σ is the standard deviation.

z = (3.4 - 2.2) / √1.44

z = 1.2 / 1.2

z = 1

Step 2: Look up the corresponding z-score in the standard normal distribution table.

The area to the left of z = 1 is approximately 0.8413.

Therefore, the answer is option A, 0.8413.