Question

1) The owner of a small deli is trying to decide whether to discontinue selling magazines. He suspects that only 8.5% of his customers buy a magazine and he thinks that he might be able to use the display space to sell something more profitable. Before making a final decision, he decides that for one day he will keep track of the number of customers that buy a magazine.

(a) Explain why this is a binomial experiment.



(b) Assuming his suspicion that 8.5% of his customers buy a magazine is correct, what is the probability that exactly 6 out of the first 13 customers buy a magazine? Give your answer as a decimal number rounded to two digits.



(c) What is the expected number of customers from this sample that will buy a magazine?

2) The systolic blood pressure (BP) of adults in the USA is nearly normally distributed with a mean of 119 and standard deviation of 21 .

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.

(a) Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places.

%

(b) Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1? Give your answer rounded to two decimal places.

%

(c) Your doctor tells you that you are in the 30th percentile (e.g. bottom 30%) for blood pressure among US adults. What is your systolic BP? Give your answer rounded to two decimal places.

mmHg

Answer 1

@) This is a Binomial experiment as there is a firaxed number Of trials (faced number being the number of customers on a particular day); the trials are independent as the one customer buying a magazine does not depend on any other customer buying the magazine ; and as there are only two possible outcomes either the customed beys the magazine er helshe cloes not 0.085 (6) Given that 8.5% of his customers buy a magazine. Henee poobability that a randomly selected customer buys the magazine Let x be the number of customers who buy a magazine out 07 13 customers. Then x fellows Binomial distribution with h=13 and p= 0.085. Therefore P(x=2)-S PQ-2)»-* = 13c266.085)* (-0.085)3-* We need to calculate P(x= 6) = 13.60.085)*(0.915] = 1716 *0.000000377) * 0.537 0.00035 ©) Expected number of customers who will buy a magazine nup = 13*0.085 - 1.105

2). Let x be the systolic blood pressure g a randomly selected Adult. Given that * follows noomal distribution with u= 119 and r = 21 = (@) Given; stage 2 high blood pressure is 160 or higher .. pooportion of adults in the USA who have stage 2 high bloog pressure - PCX > 16) 160-119 2-score comesponding to 160 V 1.95 ::P(x2160)= P(21-95)= 1-P(Z <1-95) -1-0.9744 Coom 2-table) 160-4 21 = 0.0256 .. percentage of adults who have stage 2 high blood pressure = 2.56% 140-119 <24 160-119 21 (b) pertentage proportion of adults who has systolic BP between 140 and 160 = PC1404x4160) P ( 140-4 EX-4 € 160-4)=P(140. PC1<z<1.95) - Area between eas and 1.95 under the standard normal table Area fomoto 195- Area som o to 1 = 0.4744 - 0-3413 = 0./33/ .: percentage of adults with stage, high BP = 13-31% C) Let Pso be the 30th percentile. Hence PC*<P3o) - 0-30 PC X-Z < P304) 20-30 =) P(Z<130-19)=0-30 .we need to find zo such that P(Z< 70)20.30 Whale 7 = 23,119. from 2 table 70 = -0.524 =) P30119 2-0.524 -) P303 -0.524 *21 +119. Hence your systolic BP is 108 i.e 21 107.996 Y 108