Answer:
53.94%
Step-by-step explanation:
We solve using z score formula
z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 48 points
σ is the population standard deviation = 3 points
For x = 47 points
z = 47 - 48/3
= -0.33333
Probability value from Z-Table:
P(x = 47) = 0.36944
For x = 52 points
z = 52 - 48/3
= 1.33333
Probability value from Z-Table:
P(x = 52) = 0.90879
Hence, the probability of test scores that between 47 and 52 points is calculated as:
P(x = 52) - P(x = 47)
= 0.90879 - 0.36944
= 0.53935
Therefore, the percentage of test scores that are between 47 and 52
points is given as:
0.53935 × 100
= 53.935%
Approximately to the nearest hundredth of a percent ≈ 53.94%
