Respuesta :
Answer:
a.) Minimum test score = 41
Maximum test score = 95
b.)An approximate value of the standard deviation is 9.
Step-by-step explanation:
The given set of test scores is approximately bell shaped.
The mean of the test scores, [tex]\mu[/tex] = 68
The range of the data set = 54.
a.) i.) Minimum test score = [tex]\mu - \frac{range}{2} = 68 - \frac{54}{2} = 68 - 27 = 41[/tex]
ii.) The maximum test score = [tex]\mu + \frac{range}{2} = 68 + \frac{54}{2} = 68 + 27 = 95[/tex]
b.) From the 68-95-99.7 rule, also known as the Empirical rule, tell us that an approximation of the range is 3 standard deviations either way from the mean. So from this rule we can say that the minimum can also be found from [tex]\mu - 3\sigma[/tex] and the maximum can also be approximated as [tex]\mu + 3\sigma[/tex].
From the above we can say that the range can be written as
[tex]3\sigma - (-3\sigma) = range[/tex]
∴ [tex]6\sigma = range[/tex]
∴ [tex]\sigma = \frac{range }{6} = \frac{54}{6} = 9[/tex]
Therefore an approximate value of the standard deviation is 9.
