1) Let z be a normal random variable with mean 0 and standard deviation 1. The 4th decile of z is ___.
a) 0.67 b) –1.25 c) -0.25 d) 1.28 e) 0.50
2) According to the central limit theorem, if a sample of size 50 is drawn from a population with a standard deviation of 10, the standard deviation of the distribution of the sample means would equal ___.
It would have to be negative and close to the mean.
To find the answer to these questions, we need to use the standard normal distribution table or a statistical calculator.
1) To find the 4th decile of a normal distribution, we need to find a z-score that corresponds to the 4th percentile. A z-score is a measure of how many standard deviations a particular value is from the mean. In this case, the mean is 0 and the standard deviation is 1.
Using the standard normal distribution table or a calculator, we can find the z-score that corresponds to the 4th percentile, which is approximately -1.75.
Therefore, the answer is not listed in the options provided.
2) According to the central limit theorem, the standard deviation of the distribution of the sample means is equal to the population standard deviation divided by the square root of the sample size.
In this case, the standard deviation of the population is 10 and the sample size is 50.
The standard deviation of the distribution of the sample means would be:
Standard deviation of sample means = Population standard deviation / √(sample size)
= 10 / √50
≈ 1.414.
Therefore, the answer is not listed in the options provided.