A distribution of values is normal with a mean of 165.6 and a standard deviation of 18.7. Find the probability that a randomly selected value is greater than 161.9.

Answer: the probability that a randomly selected value is greater than 161.9 is 0.977

Step-by-step explanation:

Since the distribution of values is normal, we would apply the formula for normal distribution which is expressed as

z = (x - µ) / σ

Where

x = randomly selected values.

µ = mean value

σ = standard deviation

From the information given,

µ = 165.6

σ = 18.7

We want to find the probability that a randomly selected value is greater than 161.9 ... It is expressed as

P (x > 161.9) = 1 - P (x ≤ 161.9)

For x = 161.9

z = (161.9 - 165.6) / 18.7 = - 0.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.023

P (x > 161.9) = 1 - 0.023 = 0.977