a. If X is a normal random variable with mean 10, and if the probability that X is less than 11.54 is .72 then what is the standard deviation of X?
1.75
3.50
4.20
12.25
b. If the standard deviation of a population is 36 and we take a sample of size 9, then the standard error (the standard deviation of the sample mean) is
12.00
3.00
108.00
4.00
c. According to the empirical rule, in a normal distribution about what proportion of values falls within 3 standard deviations from the mean?
99.7%
at least 89%
4.7%
2.35%
d. The mean of the sampling distribution of sample means is the same as the population mean
True
False
a. Let the standard deviation be s.
Thus, X ~ N(10, s) i.e. (X - 10)/s ~ N(0,1).
P(X < 11.54) = P[(X - 10)/s < (11.54-10)/s] = P[(X - 10)/s < 1.54/s] = (1.54/s) [(.) is the cdf of N(0,1)].
Given that, (1.54/s) = 0.72 i.e. 1.54/s = (0.72) = 0.583 i.e. s = 1.54/0.583 = 2.64.
b. Standard error = = 36/3 = 12.
c. 99.7% of the values fall within 3 standard deviations of the mean.
d. The mean of the sampling distribution of sample means is same as the population mean.
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