Question

Suppose a normally distributed random variable x has a mean of 100 and P(x < 90) = 0.30. What is the probability that x is between 90 and 110?

Select one:
a. 0.20
b. 0.40
c. 0.30
d. 0.60

Answer 1

The probability that the normally distributed random variable x is between 90 and 110 is 0.40, considering the symmetry of the normal distribution and given probabilities.

Step-by-step explanation:

To answer the question about the probability that a normally distributed random variable x is between 90 and 110 when the mean is 100 and P(x < 90) = 0.30, we need to understand certain properties of the normal distribution. Since the distribution is symmetric, if P(x < 90) is 0.30, then the probability that x is greater than the mean by the same amount (which is P(x > 110)) is also 0.30. By subtracting these probabilities from the total probability (which is 1), we can find the probability that x is between 90 and 110.

P(x is between 90 and 110) = 1 - P(x < 90) - P(x > 110)

= 1 - 0.30 - 0.30

= 1 - 0.60

= 0.40.

Therefore, the correct answer is 0.40, which corresponds to option b.