Question

In: Statistics and Probability

5. A random sample of size n = 36 is obtain from a population with µ=...

5. A random sample of size n = 36 is obtain from a population with µ= 60 and standard deviation 12 (a). Describe the sampling distribution . (b). What is P(76.5 << 85.5 )?

Expert Solution

Solution:

Given that ,

= 60

= 12

A sample of size n = 36 is taken from this population.

a)

Let be the mean of sample.

Since the sample size n > 30 , therefore

the sampling distribution of the is approximately normal with

Mean = = 60

SD = = 12/36 = 2

b)

P(76.5 < x< 85.5 )

= P(X < 85.5 ) - P(X < 76.5 )

= P[(X - )/ < (85.5 - 60)/12] - P[(X - )/ < (76.5 - 60)/12]

= P[Z < 2.125] - P[Z < 1.375]

= 0.9832 - 0.9154..Use z table

= 0.0678

orchestra answered 2 years ago

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