Answer: P(225 ≤ x ≤ 276) = 0.25
Explanation:
Since the credit ratings for applicants are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = credit ratings of applicants
µ = mean
σ = standard deviation
From the information given,
µ = 200
σ = 50
The probability of a rating that is between 225 and 276 is expressed as
P(225 ≤ x ≤ 276)
For x = 225,
z = (225 - 200)/50 = 0.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.69
For x = 276,
z = (276 - 200)/50 = 1.52
Looking at the normal distribution table, the probability corresponding to the z score is 0.94
Therefore,
P(225 ≤ x ≤ 276) = 0.94 - 0.69 = 0.25