Note that in this question, if an event has a probability of less than 5%, it is considered a rare event. For quality assurance, Eaburvalways checks the weights of its "300g chocolate bars'I before they are shipped to the respective distributors and retailers. A random sample of 10 chocolate bars was selected, and their weights {in grams} were measured as follows: weights 301.3 302.1 300.? 299.6 303.2 301.6 301.? 302.5 302.9 300.1 It is known that the weights of the chocolate bars have a population standard deviation, U of 2.5g and that the weights are normally distributed. {a} Copy and paste the above data into Minitab, find the following summary statistics of the data given. Leave your answer to the nearest 2 decimal places. [i] Sample mean {iii Sample standard deviation {b} Since Xis normally distributed and cr is known, we can model the sampling distribution E after a normal distribution. TruefFalse. :l'v {cl If the population mean u. is truly 300g, calculate the probability of ? being greater than the sample mean calculated in part {a}. Leave your answer in the nearest 2 decimal places. :lw (d) Based on answer in (c), does the quality assurance manager have reason to doubt that mean weight of chocolate bars, u, is truly 300g? Yes/No A (e) If the population mean u is truly 300g, how much would the 5th percentile of X weigh? Leave your answer to the nearest 1 decimal place. A