Answer :
Answer: P(100 ≤ x ≤ 130) = 0.43
Step-by-step explanation:
Since the scores are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = scores
µ = mean score
σ = standard deviation
From the information given,
µ = 100
σ = 20
We want to find the probability that the scores is between 100 and 130. It is expressed as
P(100 ≤ x ≤ 130)
For x = 100,
z = (100 - 100)/20 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 100,
z = (130 - 100)/20 = 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.93
Therefore,
P(100 ≤ x ≤ 130) = 0.93 - 0.5 = 0.43