Question

Given a normal distribution with μ=51 and σ=8​, and given you select a sample of

n=100​, complete parts​ (a) through​ (d).

c. What is the probability that X is above 51.3​? P(X>51.3​)=

Answer 1

The probability that X is above 51.3 in a normal distribution can be found using the z-score and normalcdf() function.

Step-by-step explanation:

To find the probability that X is above 51.3 in a normal distribution with μ=51 and σ=8, we can use the normalcdf() function. First, we find the z-score for X=51.3 using the formula: z = (X - μ) / σ. Plugging in the values, we get z = (51.3 - 51) / 8 = 0.0375. Next, we can use the normalcdf() function with the lower bound as z and the upper bound as infinity to find the probability: P(X > 51.3) = 1 - normalcdf(0.0375, E99) ≈ 0.4842. Therefore, the probability that X is above 51.3 is approximately 0.4842 or 48.42%.