Answer: 0 0.0478
Step-by-step explanation:
Since the average IQ score follows a Normal distribution, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ/√n
Where
x = IQ scores
µ = mean score
σ = standard deviation
n = number of samples
From the information given,
µ = 100
σ = 15
n = 25
the probability that the mean IQ score of 25 randomly selected people will be greater than 105 is expressed as
P(x > 105) = 1 - P(x ≤ 105)
For x = 105,
z = (105- 100)/(15/√25) = 1.67
Looking at the normal distribution table, the probability corresponding to the z score is 0.9525
P(x > 105) = 1 - 0.9525 = 0.0475
