If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x .75) is:
A) .7500
B) .7734
C) .2266
D) .2734
E) .4525

Question

If the random variable x is normally distributed with a mean equal to .45 and a standard deviation equal to .40, then P(x  .75) is:
A) .7500 
B) .7734 
C) .2266 
D) .2734 
E) .4525

Quizplus · Accepted Answer

To solve this problem, we need to standardize the random variable x using the formula z = (x - μ) / σ, where μ is the mean and σ is the standard deviation. Thus, z = (.75-.45)/.4 = .75. To find the probability P(x <. 75), we need to find the area to the left of z = .75 on a standard normal distribution table. Looking at the table, we see that the area to the left of z = .75 is .7734. However, we want the area to the right of z = .75, so we subtract .7734 from 1 to get .2266. Therefore, the answer is C.

If the Random Variable X Is Normally Distributed with a Mean