USA Today reported that 11% of all books sold are of theromance genre. If a loca
ID: 2913531 • Letter: U
Question
USA Today reported that 11% of all books sold are of theromance genre. If a local bookstore sells 316 books on a given day,what is the probability that a. fewer than 40 are romances? b. at least 25 are romances? c. between 25 and 40 are romances? d. In the solution of this problem, what is n? what is p? Whatis Q? Does it appear that both np and nq are larger than 5? Why isthis an important consideration? USA Today reported that 11% of all books sold are of theromance genre. If a local bookstore sells 316 books on a given day,what is the probability that a. fewer than 40 are romances? b. at least 25 are romances? c. between 25 and 40 are romances? d. In the solution of this problem, what is n? what is p? Whatis Q? Does it appear that both np and nq are larger than 5? Why isthis an important consideration?Explanation / Answer
USA Todayreported that 11% of all books sold are of the romance genre. If alocal bookstore sells 316 books on a given day, what is theprobability that:{Sample Size} = N = 316
{Probability} = p = 0.11
{Mean} = = N*p = (316)*(0.11) = 34.76
{Std Dev} = = Sqrt[N*p*(1 - p)] = Sqrt[(316)*(0.11)*(1 -(0.11))] = 5.562
{Normal Approx Is Applied} ----> Z = (X -)/
a. fewerthan 40 are romances?
= Prob{Z < ((40.5) - (34.76))/(5.562)} = Prob{Z < (1.032)} = 0.849
b. at least25 are romances?
= Prob{Z > ((24.5) - (34.76))/(5.562)} = Prob{Z > (-1.845)} = 0.9675
c. between25 and 40 are romances?
= Prob{((24.5) - (34.76))/(5.562) < Z < ((40.5) - (34.76))/(5.562)}
= Prob{(-1.845) < Z < (1.032)}
= (0.9675) - (0.849)
= 0.1185
d. In thesolution of this problem, what is n? what is p? What is Q? Does itappear that both np and nq are larger than 5? Why is this animportant consideration?
{Sample Size} = N = 316
{Probability} = p = 0.11
{q} = 1 - (0.11) = 0.89
{Mean} = = N*p = (316)*(0.11) = 34.76
{Std Dev} = = Sqrt[N*p*(1 - p)] = Sqrt[(316)*(0.11)*(1 -(0.11))] = 5.562
{Both "n*p" And "n*q" Are Greater Than5} ----> {Normal Approx Can BeApplied}
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