Mathematics, 30.12.2019 22:31 jfox8741

Acbs news/new york times survey found that 97% of americans believe that texting while driving should be outlawed (cbs news website, january 5, 2015).

a. for a sample of 10 americans, what is the probability that at least 8 say that they believe texting while driving should be outlawed? use the binomial distribution probability function to answer this question (to 4 decimals).

b. for a sample of 100 americans, what is the probability that at least 95 say that they believe texting while driving should be outlawed? use the normal approximation of the binomial distribution to answer this question. (to 4 decimals).

Answers: 1

Show answers

Answers

Answer from: eamccoy1

a) $P(X\geq 8)=0.0317+0.228+0.737=0.9972$

b) P(X95) =1-P(X

Step-by-step explanation:

Previous concepts

A Bernoulli trial is "a random experiment with exactly two possible outcomes, "success" and "failure", in which the probability of success is the same every time the experiment is conducted". And this experiment is a particular case of the binomial experiment.

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

The probability mass function for the Binomial distribution is given as:

$P(X)=(nCx)(p)^x (1-p)^{n-x}$

Where (nCx) means combinatory and it's given by this formula:

$nCx=\frac{n!}{(n-x)! x!}$

The complement rule is a theorem that provides a connection between the probability of an event and the probability of the complement of the event. Lat A the event of interest and A' the complement. The rule is defined by: P(A)+P(A') =1

Part a

We want this probability:

$P(X\leq 12)$

$P(X\geq 8)=P(X=8)+P(X=9)+P(X=10)$

$P(X=8)=(10C8)(0.97)^8 (1-0.97)^{10-8}=0.03174$

$P(X=9)=(10C9)(0.97)^9 (1-0.97)^{10-9}=0.2287$

$P(X=10)=(10C10)(0.97)^{10} (1-0.97)^{10-10}=0.7374$

$P(X\geq 8)=0.0317+0.228+0.737=0.9972$

Part b

We need to check if we can use the normal approximation , the conditions are:

np=100*0.97=9710 and n(1-p)=100*(1-0.97)=3

On this case the second condition is not satisfied, but the problem says that we can use it. So then if we apply the normal approximation to the binomial distribution in our case:

$X \sim N(\mu=97,\sigma=1.706)$

We can use the z score formula given by:

$z=\frac{x-\mu}{\sigma}$

And we want this probability:

$P(X95) = P(Z\frac{95-97}{1.706})= P(Z-1.17)$

And we can use the complment rule and we got:

P(X95) =1-P(X

Answer from: Quest

he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation:

Answer from: Quest

1. 0.3 •4 is the same as 4 groups of 0.32. 7•0.8 is the same as 7 groups of 0.83. it increases by 0.5 every time, so 0.5x4 it increases by 0.9 every time, so 0.9x5. 0.9•12=10.86. 0.47•5=2.35i can finish the next ones in a separate post
Can someone plz me 1 to 37 . i will earn 10 points

Can someone plz me 1 to 37 . i will earn 10 points

Another question on Mathematics

Mathematics, 21.06.2019 20:30

Diane’s bank is offering 5% interest, compounded monthly. if diane invests $10,500 and wants $20,000 when she withdrawals, how long should she keep her money in for? round to the nearest tenth of a year.

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

Which of the following shows the length of the third side, in inches, of the triangle below

Answers: 2

Answer

Mathematics, 21.06.2019 21:30

What is r i 4.5+10r=-6.5 with work pls

Answers: 1

Answer

Mathematics, 21.06.2019 22:00

Amountain climber starts a climb at an elevation of 453 feet above sea level at his first rest stop he has climbed 162 feet and by his second rest stop he has climbed another 207 feet its getting late in the day so the climber starts his way down if the climber desends 285 feet how much does he need to ascend or descend to return to the original starting point

Answers: 1

Answer

You know the right answer?

Acbs news/new york times survey found that 97% of americans believe that texting while driving shoul...

Questions

Mathematics, 26.07.2020 01:01

Joshua sells a pack of pens for $3.15, which is 5 percent more than he pays for them. Which equation will help find x, the amount he pays for a pack o...