Answer:
Step-by-step explanation:
Let x be the random variable representing the set of art exam scores. Since they are normally distributed and the population mean and population standard deviation are known, we would apply the formula,
z = (x - µ)/σ
Where
x = sample mean
µ = population mean
σ = standard deviation
From the information given,
µ = 81
σ = 10
the probability of getting a score lower than 78 is expressed as
P(x < 78)
For x = 78,
z = (78 - 81)/10 = - 0.3
Looking at the normal distribution table, the probability corresponding to the z score is 0.38
Therefore, the percentage of exam scores that are lower than Calvin's score is
0.38 × 100 = 38%
