Math 131 JK Test 2 Intersession 2014 Chapter S Problem-Binomial (table or calcul
ID: 3146631 • Letter: M
Question
Math 131 JK Test 2 Intersession 2014 Chapter S Problem-Binomial (table or calculator) would be willing to pay I. In a gro r options at restaurant Suppose this result holds true for the current probability that exactly 3 persons in this sample hold the said option. mean and standard deviation for the above probability distribution. up survey of adults, 30% of 50+ adult Americans said that they more for healthier population of 50+ adult Americans. A random sample of six a) Find the b) c) d) (6) 50+ adult Americans is selected nd the probability that at most 2 persons in this sample hold the said option Find the probabi Fi lity that at least 4 pe sons in this sample hold this oprion. Next Chapter(s) 2. Gluten sensitivit y, affects approximately 15% of people. A random sample of 800 individuals is have gluten selected. Find the probability that the number of individuals in this sample who sensitivity is: a] exactly 115, b) at least 107, c) at most 100 and d) between 100 and 1145 The GPAs of all students enrolled in a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of 29. Find the probability that the mean GPA of a random sample of 20 students selected from this university is: a) 3.10 or higher, b) 2.9 or lower, c) 2.9 to 3.1. According to a certain Foundation, US workers who had employee-provided health insurance paid an average premium of $4129 for family coverage durin 2011 uppose the premiums for family coverage paid this year by all such workers are normally distributed with a mean of $4129 and a standard deviation of $600. Find the probability that such a premium paid this year by a randomly selected such worker is: a) less than $3331, b) greater than $4453, or c) between $3331 and $4453 3. 4. 5. A calculator corporation knows the life of its PYQ machine has a normal distribution of 54 months and a standard deviation of 8 months. What should the warranty period be to replace a malfunctioning calculator if the company does not want to replace more that 2% of the PO machines soldExplanation / Answer
30% of the people in the aged 50+ sample said that they would be willing to pay more for healthier options in a restaurants ;
This sample's observation is to be considered true for the whole nation of populace who are aged 50 or more;
A random sample of 6 people is selected from the country's population:
Let's say p = probability of finding a person who agrees to pay more = 30% = 0.3
and q = probability of finding a person who doesn't agree to pay more; = 1-p = 1-0.3 = 0.7
a) probability of exactly 3 people holding this view:
6C3 p3 q3 = 6*5*4*3! / 3! 3*2 (0.3)3 (0.7)3 = 20* 0.009261 = 0.18522
Thus, probabilitt of finding 3 people out of 6 who hold this opinion = 0.18522
b) probability of at most 2 people holding this opinion =
0 people holding the opinion + 1 person holding the opinion + 2 people holding the opinion
= 6C0 p 0 q6 + 6C1 p1q5 + 6C2 p2 q4
= 1* (0.3)0 (0.7)6 + 6 (0.3)1 (0.7)5 + 6*5/2 (0.3)2 (0.7)4
= 0.117649 + 0.302526 + 0.324135
= 0.74431
c) at least 4 people holding the opinion =
1- ( up to 2 people + exactly 3 people )
= 1 - 0.74431 (from asnwer B) - 0.18522 ( from answer A)
= 0.07047;
d) mean = n*p = 6*0.3 = 1.8;
standard deviation = square root of variance ;
Variance = npq = 6*0.3*0.7 = 1.26
standard deviation = sqrt(1.26) = 1.122497 ;