Question

In: Statistics and Probability

X has a distribution with mean = 70 and standard deviation = 20. The sample size...

X has a distribution with mean = 70 and standard deviation = 20. The sample size is 16.

Find P(66 < or equal to x bar < or equal to 71)

Expert Solution

Solution :

Given that ,

= 70

= 20

A sample of size n = 16 is taken from this population.

Let be the mean of sample.

The sampling distribution of the is approximately normal with

Mean = = 70

SD = = 20/16 = 5

Find, P(66 < < 71)

= P( < 71) - P( < 66)

= P[( - )/ < (71 - 70)/5] - P[( - )/ < (66 - 70)/5]

= P[Z < 0.2] - P[Z < -0.8]

= 0.5793 - 0.2119 .........(use z table)

= 0.3674

P(66 < < 71) = 0.3674

orchestra answered 2 years ago

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