Question

11) A student takes a true-false test that has 20 questions and guesses randomly at each answer. Let X be the number of questions answered correctly. Find P(19 or more)  

A) 0.1719

B) 0.006

C) 0.00002

D) 0.07

12) It is estimated that 35% of households own a riding lawn mower. A sample of 10 households is studied. What is the probability that more than 7 of these own a riding lawn mower? (hint: you can use binomial or independent probability.)

15) A group of 10 male and 4 female students is talking about going out for pizza. If 50% of the male students actually go and 25% of the female students actually go, find the probability that a random student who goes out for pizza is female.

16) A lot of 1000 components contain 300 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn is defective, and let B be the event that the second component drawn is defective. Find P(A and B).

17) A paint manufacturer discovers that the mean volume of paint in a gallon-sized

pail is 1 gallon with a standard deviation of 0.1 gallons. The paint volumes are

approximately bell-shaped (normally distributed). Estimate the percent of pails

with volumes between .70 gallons and 1.30 gallons.

21) The average length of crocodiles in a swamp is 10.5 feet. If the lengths are normally distributed with a standard deviation of 1.3 feet, find the probability that a crocodile is more than 10 feet long.

Answer 1

11) X is the number of questions correctly answered out of 20. So X ~ Binomial (20, p) where p = probability of success = probability of getting answer correct = 1/2 [as there are only two options true/false]

So

   as we first select which k questions to be correct then multiply by prob of them being correct by p^k x prob of rest being wrong = (1-p)^(20-k)

So,

So option C

12) X be the number of households that own a lawn mower out of 10 then X ~ (10,p) where p = probability of success = probability of owning a lawn mower = 35/100 = 7/20

So again similar to previous problem,

15) Let G = event that a person goes out

M = event that person is male

F = event that a person is female

We have to find P(F | G)

By Bayes theorem we have

We know that P(G|F) = 25/100 = 1/4

And as there are 10 males and 4 females so P(F) = 4/14

By law of total probability ,

P(G) = P(G|M)P(M) +P(G|F)P(F) = (1/2)x(10/14) + (1/4)x(4/14) = 24/56 = 3/7

So,

16)

P(A and B) = probability that both the randomly chosen components are defective = no. of ways of choosing two components from defective ones / no. of ways of choosing 2 components from all population

So, P(A and B) =

Thank you! We are advised to do minimum one question or four parts. I have already done 4 separate questions so i would advise you to pose the rest as a separate question. Please rate positively if satisfied!