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The number of accidents per week at a hazardous intersection varies with mean 2.2 and standard deviation of 1.4. The distribution takes only integers and most definitely not normal. Let x-bar be the mean of accidents per week at the intersection during one year (52 weeks). What is the approximate probability that x-bar is less than 2

Respuesta :

Answer:

Approximate probability that [tex]\overline{X}[/tex] is less than 2 = 0.1515

Step-by-step explanation:

Given -

Mean [tex](\nu )[/tex] = 2.2

Standard deviation [tex](\sigma )[/tex] = 1.4

Sample size ( n ) = 52

Let  [tex]\overline{X}[/tex] be the mean of accidents per week at the intersection during one year (52 weeks) .

probability that [tex]\overline{X}[/tex] is less than 2 =

[tex]P(\overline{X}< 2)[/tex]  = [tex]P(\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}}< \frac{2 - 2.2 }{\frac{1.4}{\sqrt{52}}})[/tex]   Putting [tex](Z =\frac{\overline{X} - \nu }{\frac{\sigma }{\sqrt{n}}})[/tex]

                 = [tex]P(Z< - 1.03)[/tex]    ( Using Z table )

                 = 0.1515

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