Given an infinite population with a mean of 75 and a standard deviation of 12, t

Question

Given an infinite population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations, taken at random from this population, is less than 78 is: a. 0.9332 b. 0.5987 c. 1.5000 d. None of these choices. The probability density function f(x) of a random variable X that has a uniform distribution between a and b is a. (b + a)/2 b. 1/b 1/a c. (a b)/2 d. None of these choices. Which of the following is the method statisticians use to draw the best fitting straight line through the data on a scatter diagram? a. The fit best method. b. The least squares method. c. The point-intercept method. d. None of these choices.

Explanation / Answer

1) std error of mean =std deviation/(n)1/2 =12/(36)1/2 =2

therefore P(X<78)=P(Z<(78-75)/2)=P(Z,<1.5)=0.9332

option A is correct

2)probabilty density function of uniform distribution =1/(b-a)

therefore option D

3)option b; the least square method

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