Answer: the minimum score required for a letter of recognition is 27.8
Step-by-step explanation:
Suppose ACT Mathematics scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = ACT Mathematics scores.
µ = mean score
σ = standard deviation
From the information given,
µ = 21.3
σ = 5.3
The probability of students whose scores are in the top 11 % would be be (1 - 11/100) = (1 - 0.11) = 0.89
Looking at the normal distribution table, the z score corresponding to the probability value is .23
Therefore,
1.23 = (x - 21.3)/5.3
Cross multiplying by 8.6, it becomes
1.23 × 5.3 = x - 21.3
6.519 = x - 21.3
x = 6.519 + 21.3
x = 27.8 to the nearest whole number
