Answer:
a. 0.40198
b. 0.36049
c. 0.20046
Explanation:
To solve for this we make use of the z score formula.
z-score formula is
z = (x-μ)/σ,
where
x is the raw score
μ is the population mean
σ is the population standard deviation.
a. Compute the probability of a value between 75.0 and 90.0.
For x = 75
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 75 - 80/ 14
z = -0.35714
Using the z score table to find the probability
P-value from Z-Table:
P(x = 75) = P(z = -0.35714)
= 0.36049
For x = 90
z = 90 - 80/14
z = 0.71429
Using the z score table to find the probability
P-value from Z-Table:
P(x = 90) = P(z = 0.71429)
= 0.76247
The probability of a value between 75.0 and 90.0 is:
75 < x < 90
= P( x = 90) - P(x = 75)
= 0.76247 - 0.36049
= 0.40198
Therefore, probability of a value between 75.0 and 90.0 is 0.40198
b. Compute the probability of a value of 75.0 or less.
For x = 75
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 75 - 80/ 14
z = -0.35714
Using the z score table to find the probability
P-value from Z-Table:
P(x ≤ 75) = 0.36049
c. Compute the probability of a value between 55.0 and 70.0.
For x = 55
From the question, we know that
mean of 80.0 and a standard deviation of 14.0.
z = (x - μ)/σ
z = 55 - 80/ 14
z = -1.78571
Using the z score table to find the probability
P-value from Z-Table:
P(x = 55) = P(z = -1.78571)
= 0.037073
For x = 70
z = 70 - 80/14
z = -0.71429
Using the z score table to find the probability
P-value from Z-Table:
P(x = 70) = P(z = -0.71429)
= 0.23753
The probability of a value between 55.0 and 70.0 is:
55 < x < 70
= P( x = 70) - P(x = 55)
= 0.23753 - 0.037073
= 0.200457
Approximately to 4 decimal place = 0.20046