Answer: the minimum score required for recruitment is 669
Step-by-step explanation:
Suppose SAT Mathematics scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = SAT Mathematics scores.
µ = mean score
σ = standard deviation
From the information given,
µ = 518
σ = 113
The probability value for the top 9% would be (1 - 9/100) = (1 - 0.09) = 0.91
Looking at the normal distribution table, the z score corresponding to the probability value is 1.34
Therefore,
1.34 = (x - 518)/113
Cross multiplying by 113, it becomes
1.34 × 113 = x - 518
151.42 = x - 518
x = 151.42 + 518
x = 669 to the nearest whole number.
