1. The host probability distribution (e.g., wages of individuals) whose mean you wish to estimate is not normally distributed, and yet your analysis of the mean of a random sample involves the normal distribution. Explain why.
2. Suppose Z1,…, Z7 are i.i.d., with the distribution N(0, 1). Determine Pr[z bar≤ .8].
3. Suppose X1,…, X7 are i.i.d., with the distribution N(25, 18). Determine Pr[x bar≤ 27].
4. Suppose Z1,…, Z7 are i.i.d., with the distribution N(0, 1). What is the probability that they all yield values less than 1.8?
a. Pr[Z≤.8]-Pr[Z>-0.2]=Pr[Z≤.8]-(1-Pr[Z≤.2])=0.7881-(1-0.5793)=0.3074b. (27-25)/(18^0.5)=2/4.24264068712=0.47c. Pr[Z≤1.8]=0.9641
