Question

Some player heights are normally distributed with a mean 5.0 feet and a standard deviation of 0.3 feet. Let X. equals the height of a randomly selected student from this set.

Find P(4.7≤x≤5.3)=??

Answer 1

P(4.7≤x≤5.3)≈0.6827≈68.27%

Explanation:

Notice that 4.7 is 1 standard deviation below the mean (μ) and 5.3 is 1 standard deviation above the mean. Thus, by the Empirical Rule, ±1σ represents about 68.27% of the data in a normal distribution, meaning that P(4.7≤x≤5.3)≈0.6827