Question

X is a normally distributed random variable with mean 90 and standard deviation 1. What is the probability that X is between 89 and 91?

A. 0.6827
B. 0.9545
C. 0.3413
D. 0.4772

Answer 1

To find the probability that X is between 89 and 91, we can use the z-score formula. The z-score calculates how many standard deviations away a particular value is from the mean. The probability that X is between 89 and 91 is 0.6827 (A).

Step-by-step explanation:

To find the probability that a normally distributed random variable X is between 89 and 91, we can use the z-score formula. The z-score calculates how many standard deviations away a particular value is from the mean. In this case, the mean is 90 and the standard deviation is 1. To find the z-scores for 89 and 91:

1. Subtract the mean (90) from each value (89 and 91): -1 and 1.
2. Divide each difference by the standard deviation (1): -1/1 = -1 and 1/1 = 1.

The area under the normal curve between -1 and 1 is approximately 0.6827. Therefore, the probability that X is between 89 and 91 is 0.6827 (A).