Answer: the minimum score required for an A grade is 91
Step-by-step explanation:
Since the scores on the test are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = scores on the test.
µ = mean score
σ = standard deviation
From the information given,
µ = 81.8
σ = 7.8
The probability value for the scores in the top 11% would be (1 - 11/100) = (1 - 0.11) = 0.89
Looking at the normal distribution table, the z score corresponding to the probability value is 1.23
Therefore,
1.23 = (x - 81.8)/7.8
Cross multiplying by 114, it becomes
1.23 × 7.8 = x - 81.8
9.594 = x - 81.8
x = 9.594 + 81.8
x = 91 rounded to the nearest whole number.
