To find the probability that X is between 45 and 54, we need to calculate the z-scores for each of these values first.
Z-score for 45:
Z = (45 - 50) / 2 = -2.5
Z-score for 54:
Z = (54 - 50) / 2 = 2
Next, we need to find the cumulative probability for each z-score using a standard normal distribution table.
For Z = -2.5, the cumulative probability is 0.0062.
For Z = 2, the cumulative probability is 0.9772.
Finally, to find the probability that X is between 45 and 54, we subtract the cumulative probability of the lower z-score from the cumulative probability of the higher z-score.
0.9772 - 0.0062 = 0.9710
Therefore, the probability that X is between 45 and 54 is 0.9710.
Given that X is a normally distributed random variable with a mean of 50 and a standard deviation of 2, find the probability that X is between 45 and 54.
0.9898
0.8865
0.8958
0.9710
1 answer
1 answer