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The price-earnings ratios of a sample of stocks have a mean value of 13.5 and a standard deviation of 2. If the ratios have a bell shaped distribution, what can we say about the proportion of ratios that fall between 9.5 and 17.5?"

Respuesta :

Answer:

proportion of ratios = 0.9545

so interval contain 95% ratio

Explanation:

given data

mean [tex]\mu[/tex] =  13.5

standard deviation [tex]\sigma[/tex]  = 2

solution

we have given P ( 9.5 < x < 17.5 )

so proportion of ratios is

[tex]P ( \frac{9.5-\mu }{\sigma } < \frac{x-\mu }{\sigma } < \frac{17.5-\mu }{\sigma} )[/tex]   ...........1

put here mean and SD value

[tex]P ( \frac{9.5-13.5 }{2 } < \frac{x-\mu }{\sigma } < \frac{17.5-13.5}{2} )[/tex]

and it will be

P ( -2 <  Z  < 2 )

so it is

P ( Z < 2 ) - P ( Z < -2 )

and

proportion of ratios = 1 - 2 × ( Z > 2 )

proportion of ratios = 1 - 2  × 0.0227

proportion of ratios = 0.9545

so interval contain 95% ratio

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