Which of the following statement is correct?(2 MARKS)

a)Any Normal distribution is a continuous probability distribution with mean 0 and standard deviation 1.

b)A Standard Normal distribution is a continuous probability distribution with mean 0 and variance 1.

c)The area under a Normal curve is equals to 1 if and only if that curve is a Standard Normal curve.

d)A Standard Normal distribution is a discrete probability distribution with mean 0 and standard deviation 1.

Which of the following statement on the Central Limit Theorem is correct, assuming that the population mean and standard deviation are known? (3 MARKS)

a)Means are always normally distributed (approximately) for sufficiently large sample sizes (n 30)providedthat the distribution of the population of data values is normal.

b)Means are always normally distributed (approximately) for sufficiently large sample sizes (n 30)regardlessof the distribution of the population of data values.

c)A random variable that is not normally distributed becomes approximately normally distributed if repeated samples of size n 30 are drawn to estimate the sample mean.

d)A random variable becomes approximately normally distributed if repeated samples of size n 30 are drawn to estimate the sample standard deviation.