Question

Find the required probability for the area to the left of X = 42, under normal curve with mean = 40 and standard deviation = 2.2847. (Round to two decimals)

0.79

0.63

0.83

0.81

Answer 1

To calculate the probability of X=42 under the normal distribution with mean 40 and standard deviation 2.2847, we find the z-score and use the z-table to determine the area to the left. The correct probability is approximately 0.81.

Step-by-step explanation:

The question requires us to find the required probability for the area to the left of X = 42, under a normal distribution curve, where the mean (μ) is 40 and the standard deviation (σ) is 2.2847. To find this probability, we must calculate the z-score using the formula:

Z = (X - μ) / σ

Substituting the given values:

Z = (42 - 40) / 2.2847 ≈ 0.875

We then use the z-table to find the area under the normal curve to the left of the calculated z-score. Consulting the z-table, we find that the area to the left of a z-score of 0.875 is approximately 0.81. As such, the required probability is 0.81. Thus, the mention correct option in Final Part of our choice would be 0.81.