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