The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?

Select one:
a. 72
b. 77.5
c. 83
d. 72

Question

The test scores of 1,200 students are normally distributed with a mean of 83 and a standard deviation of 5.5. Under which interval did approximately 978 students score?

Select one:
a. 72
b. 77.5
c. 83
d. 72

vankhanh · Answer

Using the  Empirical Rule , it is found that the interval in which approximately  978 students  scored was:   A.  72 < x < 88.5.    What does the Empirical Rule state?    It states that, for a  normally distributed  random variable:   Approximately  68%  of the measures are  within 1  standard deviation of the mean.    Approximately  95%  of the measures are  within 2  standard deviations of  the mean.    Approximately  99.7%  of the measures are  within 3  standard deviations of the mean.     The  percentage  that 978 is of 1200 is:  978/1200 x 100% = 81.5%.    Considering the  symmetry  of the normal distribution , two outcomes  are possible involving 81.5% of the measures:   Between one standard deviation below the mean and two above, which in the context of this problem is  between 77.5 and 94 .    Between two standard deviations below the mean and one above, which in the context of this problem is  between 72 and 88.5,  which is  option A  in this problem.     More can be learned about the  Empirical Rule  at https://brainly.com/question/24537145  #SPJ1

What does the Empirical Rule state?

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