Question 1 1 pts The Central Limit Theorem plays a key role in statistical inference. Assume that a random sample is collected from some probability distribution (perhaps a Poisson, a lognormal, a Normal, a beta, etc., but we don't know what it is). The Central Limit Theorem says that for a large enough random sample: 0 the distribution of possible averages we might observe from a random sample will closely resemble a Normal distribution, regardless of the shape of whatever probability distribution is making the data 0 the histogram of observed data values will closely resemble a Normal distribution 0 the histogram of observed data values will closely resemble whatever probability distribution generating the data 0 the distribution of possible averages we might observe from a random sample will closely resemble a Normal distribution, as long as the shape of whatever probability distribution is making the data is approximately Normal 0 the distribution of possible averages we might observe from a random sample will closely resemble a Normal distribution as long as all data values are positive Question 2 1 pts The EX6.WINE dataset in the regclass package contains chemical characteristics of 2700 wines, one of which is the pH library(regclass); data(EX6. WINE); hist(EX6. WINE$PH) Some probability distribution is responsible for generating the pH values of these wines, but we don't know it is. However, we don't particularly care since we only want a 95% confidence interval for its average. Use t.test() to make a 95% confidence interval for "mu", the average of whatever probability distribution is making the data. Report the lower limit of the 95% confidence interval. Copy/paste all digits and Canvas will take care of the rounding.The histogram of the pH values of the wines looks roughly symmetric. Histogram of EX6.WINE$pH 200 400 600 800 Frequency O 2.8 3.0 3.2 3.4 3.6 3.8 EX6.WINESpH For the Central Limit Theorem to be "in effect" and for us to make a 95% confidence interval for "mu", we need enough data. However "enough data" depends on the shape of histogram. With 2700 datapoints it doesn't matter what the distribution looks like...that's always enough data. However, in general, for a roughly symmetric distribution like what we see here, we'd need at least ___ observations for the Central Limit Theorem to be in effect