Question

Let z be a normal random variable with mean 0 and standard deviation 1. What is P(z > -1.1)?

		-0.8643
		0.8643
		-0.1357
		0.1357

If all possible random samples of size n are taken from a population that is not normally distributed, and the mean of each sample is determined, what can you say about the sampling distribution of sample means?

		It is approximately normal provided that n is large enough.
		It is positively skewed.
		It is negatively skewed.
		None of the above

Answer 1

Solution:-

1) Let z be normal random variable with mean 0 and standard deviation 1. Then P(z>-1.1)=?

-------> P(z>-1.1) = 1- P(z<= -1.1)

By Z- Distribution table,

P(z<= -1.1) = 0.13567

Hence, P(z>-1.1) = 1 - 0.13567 = 0.86433

2)

-------> It is approximately normal distribution provided that 'n' is large enough.