Question

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

Answer 1

Approximate probability that
`\overline{X}` is less than 2 = 0.1515

Explanation:

Given -

Mean
`(\\u )` = 2.2

Standard deviation
`(\sigma )` = 1.4

Sample size ( n ) = 52

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

probability that
`\overline{X}` is less than 2 =

`P(\overline{X}< 2)` =
`P(\frac{\overline{X} - \\u }{(\sigma )/(√(n))}< (2 - 2.2 )/((1.4)/(√(52))))` Putting
`(Z =\frac{\overline{X} - \\u }{(\sigma )/(√(n))})`

=
`P(Z< - 1.03)` ( Using Z table )

= 0.1515