Question

6.3.13 Assigned Media Assume that adults have IQ scores that are normally distributed with a mean of 106 and a standard deviation - 15 Find the probity that a randomly selected adult has an IQ less than 123 Click to view page of the table. Oick to view 2002 otthe table The probability that a randomly selected adut has an IQ less than 123 (Type an integer or decimal rounded to four decimal places as needed)

Answer 1

Here, μ = 105, σ = 15 and x = 123. We need to compute P(X <= 123). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z = (123 - 105)/15 = 1.2

Therefore,
P(X <= 123) = P(z <= (123 - 105)/15)
= P(z <= 1.2)
= 0.8849