Answer: the minimum score required for an A grade is 81
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 = 70.8
σ = 8.6
The probability value for the top 13% of the scores would be (1 - 13/100) = (1 - 0.13) = 0.87
Looking at the normal distribution table, the z score corresponding to the probability value is 1.13
Therefore,
1.13 = (x - 70.8)/8.6
Cross multiplying by 8.6, it becomes
1.13 × 8.6 = x - 70.8
9.718 = x - 70.8
x = 9.718 + 70.8
x = 81 to the nearest whole number
