Question

In: Statistics and Probability

Find values a and b, such that 95% of the time, X lies between a and...

Find values a and b, such that 95% of the time, X lies between a and b. In other words, find a and b so that P(a <X < b) =:95. Round to 3 decimal places.

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Expert Solution

SOLUTION:

From given data,

Find values a and b, such that 95% of the time, X lies between a and b. In other words, find a and b so that P(a <X < b) =:95.

95% of the time, X lies between a and b

P( - 2 < X < + 2 ) = 95%

95% = 95/100 = 0.95

1 - 0.95 = 0.05

0.05 / 2 = 0.025

at the value of 0.025 the probability (Area under curve) is 1.960 then

P(-1.960 < < 1.960) = 0.95

by comparing with below

P(a < X < b) =0.95

a = -1.960

b = +1.960

orchestra answered 2 years ago

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