Answer: The number of scores between 21 and 25 is 2872
Step-by-step explanation:
Since the test scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - u)/s
Where
x = test scores
u = mean test score
s = standard deviation
From the information given,
u = 23
s = 4
We want to find the probability test scores between 21 points and 25. It is expressed as
P(21 lesser than or equal to x lesser than or equal to 25)
For x = 21,
z = (21 - 23)/4 = - 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.30854
For x = 25,
z = (25 - 23)/4 = 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.69146
P(21 lesser than or equal to x lesser than or equal to 25)
= 0.69146 - 0.30854 = 0.38292
The number of scores between 21 and 25 would be
0.38292 × 7500 = 2872
