Mathematics

Question

The mean of a set of credit scores is 690 and 14. Which credit score is within a z-score of 3.3?
634
640
720
750

2 Answer

  • The answer is c) 720.
  • Answer:

    C. 720.

    Step-by-step explanation:

    We have been given that the mean of a set of credit scores is 690 and standard deviation is 14.

    To find the credit score that is within a z-score of 3.3 we will use z-score formula.

    [tex]z=\frac{x-\mu}{\sigma}[/tex], where,

    [tex]z=\text{z-score}[/tex],

    [tex]x=\text{Raw score}[/tex],

    [tex]\mu=\text{Mean}[/tex],

    [tex]\sigma=\text{Standard deviation}[/tex].

    Upon substituting our given values in above formula we will get,

    [tex]3.3=\frac{x-690}{14}[/tex]

    Let us multiply both sides of our equation by 14.

    [tex]3.3*14=\frac{x-690}{14}*14[/tex]

    [tex]46.2=x-690[/tex]

    Let us add 690 to both sides of our equation.

    [tex]46.2+690=x-690+690[/tex]

    [tex]736.2=x[/tex]

    Upon looking at our given values we can see that credit score 720 is within a z-score of 3.3, while 750 is above our given z-score, therefore, option C is the correct choice.

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