15) Suppose a random sample of n 64 measurements is selected from a population w

Question

15) Suppose a random sample of n 64 measurements is selected from a population with mean 65 and standard deviation 12. Find the probability that falls between 65.75 and 68.75. ,3023 16) A random sample of n- 600 measurements is drawn from a binomial population with probability of success .08. Give the mean and the standard deviation of the sampling distribution of the sample proportion, A) .92; .003 B) .08; .003 C) .92; .011 D) .08; .011 17) A random sample of n 400 measurements is drawn from a binomial population with probability of success .21. Give the mean and the standard deviation of the sampling distribution of the sample proportion, p. A) .21: .008 B) .21 .02 C) .79; .02 D) .79; .008 Suppose a random sample of n measurements is selected from a binomial population with probability of success p .32. Given n 400, describe the shape, and find the mean and the

Explanation / Answer

Q15.

Mean ( u ) =65
Standard Deviation ( sd )= 12/ Sqrt(n) = 1.5
Number ( n ) = 64
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
To find P(a <= Z <=b) = F(b) - F(a)
P(X < 65.75) = (65.75-65)/12/ Sqrt ( 64 )
= 0.75/1.5
= 0.5
= P ( Z <0.5) From Standard Normal Table
= 0.69146
P(X < 68.75) = (68.75-65)/12/ Sqrt ( 64 )
= 3.75/1.5 = 2.5
= P ( Z <2.5) From Standard Normal Table
= 0.99379
P(65.75 < X < 68.75) = 0.99379-0.69146 = 0.3023                  

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