Answer:
a) 15.866%
b) 0.68268
Explanation:
The scores for all the sixth graders at Roberts School on a statewide test are normally distributed with the mean of 76 and a standard deviation of 10.
We solve the above question using z score formula
= z = (x-μ)/σ, where
x is the raw score
μ is the population mean = 76
σ is the population standard deviation = 10
a) What percent of the scores were below 66?
x < 66
Hence,
z = 66 - 76/10
z = -1
Probability value from Z-Table:
P(x<66) = 0.15866
Converting to Percentage =
0.15866 × 100
= 15.866%
b) What is the probability that a student earned a score between 66 and 86?
For x = 66
Hence,
z = 66 - 76/10
z = -1
Probability value from Z-Table:
P(x≤ 66) = 0.15866
x = 66 = 0.15866
For x = 86
Hence,
z = 86 - 76/10
z = 1
Probability value from Z-Table:
P(x≤ 86) = 0.15866
x = 66 = 0.15866
Probability value from Z-Table:
P(x = 86) = 0.84134
The probability that a student earned a score between 66 and 86 is calculated as:
P(x = 86) - P(x = 76)
= 0.84134 - 0.15866
= 0.68268