1.Let X₁be a random variable from a distribution with a mean of 8 and a standard deviation of 6 and X₂be a random variable from a distribution with a mean of 7 and a standard deviation of 5.

(a)For independent samples of sizes n₁= 3 and n₂= 6, find the mean and standard deviation of.

(b)Do X₁and X₂have to be normally distributed for your answer to part(a)to be valid? Explain.

(c)Can you conclude that the variablein part(a)is normally distributed? Explain.

(d)SupposeX₁and X₂are normally distributed,determine the percentage of all pairs of independent samples of sizes n₁= 3 and n₂= 6 with the property that the difference between the sample means,,is between -9 and 11.