Answer :
Answer: P(200 ≤ x ≤ 275) = 0.4332
Step-by-step explanation:
Since the credit ratings are normally distributed, we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = credit ratings for applicants
µ = mean
σ = standard deviation
From the information given,
µ = 200
σ = 50
The probability of a rating that is between 200 and 275 is expressed as
P(200 ≤ x ≤ 275)
For x = 200,
z = (200 - 200)/50 = 0
Looking at the normal distribution table, the probability corresponding to the z score is 0.5
For x = 275,
z = (275 - 200)/50 = 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.9332
Therefore,
P(200 ≤ x ≤ 275) = 0.9332 - 0.5 = 0.4332
The probability of a rating that is between 200 and 275 is,
[tex]P(200 \leq x \leq 275) = 0.4332[/tex]
Since the credit ratings are normally distributed.
Now, apply the formula for normal distribution . Which is shown below,
[tex]z=\frac{x-\mu}{\sigma}[/tex]
Where x represent credit ratings for applicants , µ is mean and σ is standard deviation.
From the given information, µ = 200 and σ = 50
For x = 200,
[tex]z=\frac{200-200}{50} =0[/tex]
In normal distribution table, the probability corresponding to the zero z score is 0.5 .
For x = 275,
[tex]z=\frac{275-200}{50} =1.5[/tex]
In normal distribution table, the probability corresponding to the z score of 1.5 is 0.9332
Thus, [tex]P(200 \leq x \leq 275) = 0.9332 - 0.5 = 0.4332[/tex]
Hence, The probability of a rating that is between 200 and 275 is,
[tex]P(200 \leq x \leq 275) = 0.4332[/tex]
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