Answer:
First option is correct.
Proportion of students with scores less than 80 is 0.7794
Explanation:
We first need to standardize the score 80.
The standardized score for 80 is the value minus the mean then divided by the standard deviation.
z = (x - xbar)/σ = (80 - 74.3)/7.4 = 0.77
To determine the probability of scoring less than 80, P(x < 80) = P(z < 0.77)
We'll use data from the normal probability table for these probabilities
P(x < 80) = P(z < 0.77) = 1 - P(z ≥ 0.77) = 1 - P(z ≤ -0.77) = 1 - 0.22065 = 0.77935 = 0.7794.
Option A
"0.7794" would be a proportion of students scored below 80 points
Given values are:
Mean = 74.3
Standard deviation = 7.4
The standardized score for 80:
→ [tex]z = \frac{x - \bar x}{\sigma}[/tex]
By substituting the values,
[tex]= \frac{80-74.3}{7.4}[/tex]
[tex]= 0.77[/tex]
hence,
The probability will be:
→ [tex]P(x<80) = P(z<0.77)[/tex]
[tex]= 1-P(z \geq 0.77)[/tex]
[tex]= 1-P(z \leq -0.77)[/tex]
[tex]= 1-0.22065[/tex]
[tex]= 0.7794[/tex]
Thus the above answer i.e., "Option a" is correct.
Find out more information about probability here:
https://brainly.com/question/24756209
