Question

# 5-1. Consider a random sample of size 36 from a normal distribution (population) with a mean...

5-1. Consider a random sample of size 36 from a normal distribution (population) with a mean of 10 and a standard deviation of 6. Which of the following statement is false?

(a) The mean of X¯ is 10. (b) The standard deviation of X¯ is 1. (c) X¯ approximately follows a normal distribution. (d) There is an incorrect statement in the alternatives above.

5-2. Let X1, . . . , X36 be a random sample from Bin(36, 0.5). Which of the following statements is false?

(a) The mean of X¯ is 18. (b) The standard deviation of X¯ is 1/3. (c) The mean of P36 i=1 Xi is 648. (d) The standard deviation of P36 i=1 Xi is 18. (e) X¯ approximately follows a normal distribution.

Solution :

1) mean = = 10

standard deviation = = 6

n = 36  = = 10  = / n = 6 / 36 = 1

a)  False statement is -(d) There is an incorrect statement in the alternatives above.

2)

b) approximately follows a normal distribution.

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