You are to take a multiple-choice exam consisting of 100 questions with 5 possible responses to each question. Suppose that you have not studied and so must guess (select one of the five answers in a completely random fashion) on each question. Let x represent the number of correct responses on the test. (a) What is your expected score on the exam? (Hint: Your expected score is the mean value of the x distribution.) (b) Compute the variance and standard deviation of x. Variance = Standard deviation =

Answers

Answer 1

Answer:

Answer:

a) 20

b) Variance 16, standard deviation 4

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guesses the answer correctly, or you do not. The probability of guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

The standard deviation of the binomial distribution is:

$√(V(X)) = √(np(1-p))$

100 questions

So n = 100.

You guess

5 options, one correct. So $p = (1)/(5) = 0.2$

(a) What is your expected score on the exam?

$E(X) = np = 100*0.2 = 20$

(b) Compute the variance and standard deviation of x.

Variance:

$V(X) = np(1-p) = 100*0.2*0.8 = 16$

Standard deviation:

$√(V(X)) = √(16) = 4$

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A flywheel is attached to a crankshaft by 12 bolts, numbered 1 through 12. Each bolt is checked to determine whether it is torqued correctly. Let A be the event that all the bolts are torqued correctly, let B be the event that the #3 bolt is not torqued correctly, let C be the event that exactly one bolt is not torqued correctly, and let D be the event that bolts #5 and #8 are torqued correctly. State whether each of the following pairs of events is mutually exclusive.a. A and Bb. B and Dc. C and Dd. B and C

Answers

Answer:

Mutually exclusive

Not Mutually exclusive

Step-by-step explanation:

From the question we are told that

The number of bolt is n = 12

The event that all the bolt are torqued correctly is A

The event that the 3rd bolt is not torqued correctly is B

The event that exactly one bolt is not torqued correctly is C

The event that the $4^(th)$ and $8^(th)$ are torqued correctly is D

Generally for an event to be mutually exclusive it means that both event can not occur at the same time

Considering a

The A and B are mutually exclusive because they can not occur at the same time

Considering b

The event B and D are not mutually exclusive because they can occur at the same time

Considering c

Event C and D are not mutually exclusive because they can occur at the same time

Considering d

Event B and C are not mutually exclusive because they can occur at the same time

Final answer:

Event pairs A and B, and B and C are mutually exclusive. Event pairs B and D and C and D are not mutually exclusive.

Explanation:

In order to determine whether two events are mutually exclusive, we need to check if they can both occur at the same time. If the occurrence of one event necessarily means that the other event cannot occur, then the events are mutually exclusive. Let's analyze each pair of events:

a. A and B: These events are mutually exclusive because if all the bolts are torqued correctly (event A), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

b. B and D: These events are not mutually exclusive because it is possible for the #3 bolt to be not torqued correctly (event B) while the bolts #5 and #8 are torqued correctly (event D).

c. C and D: These events are not mutually exclusive because it is possible for exactly one bolt to not be torqued correctly (event C) while the bolts #5 and #8 are torqued correctly (event D).

d. B and C: These events are mutually exclusive because if exactly one bolt is not torqued correctly (event C), then it is not possible for the #3 bolt to be not torqued correctly (event B) at the same time.

Learn more about Mutually exclusive events here:

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lled a 12:3:112:3:1 ratio. Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2:131F2:131 white squash, 3434 yellow squash, and 1010 green squash. Are these data consistent with a 12:3:112:3:1 dominant epistatic model of genetic inheritance( white being dominant)? The null hypothesis for the chi‑square goodness‑of‑fit test is

Answers

Here is the full question:

When a species has several variants of a phenotype passed on from generation to generation, we can form a hypothesis about the genetics of the trait based on Mendelian theories of genetic inheritance. For example, in a two-gene dominant epistatic model, the first gene masks the effect of the second gene, leading to the expression of three phenotype variants. Crossing the dominant and recessive homozygote lines would result in a second generation represented by a mix of dominant, intermediate, and recessive phenotype variants in the expected proportions: and respectively, also called a 12:3: 1 ratio.

Such a model can provide the basis for the null hypothesis in a significance test. A cross of white and green summer squash plants gives the number of squash in the second generation F2: 131 white squash, 34 yellow squash, and 10 green squash. Are these data consistent with a 12: 3: 1 dominant epistatic model of genetic inheritance( white being dominant)?

The null hypothesis for the chi-square goodness-of-fit test is

Answer:

The null hypothesis for the chi-square goodness-of-fit test is :

$\mathbf{H_o:p_(white) = (12)/(16), p_(yellow) = (3)/(16); p_(green) = (1)/(16) }$

Step-by-step explanation:

The objective of this question is to state the null hypothesis for the chi-square goodness-of-fit test.

Given that:

There are three colors associated with this model . i,e White , yellow and green and they are in the ratio of 12:3:1

The total number of these color traits associated with this model = 12 + 3 + 1 = 16

Thus ;

The null hypothesis for the chi-square goodness-of-fit test is :

$\mathbf{H_o:p_(white) = (12)/(16), p_(yellow) = (3)/(16); p_(green) = (1)/(16) }$

The sphere at the right fits snugly inside a cube with 4-in. edges. What is the approximate volume of the space between the sphere and cube?

Answers

As given by the question

There are given that the inside edge is 4 in.

Now,

Since sphere fits snugly inside a cube therefore diameter of sphere will be equal to side of the cube

So,

$\begin{gathered} \text{diameter}=4\text{ inches} \n \text{radius}=(dameter)/(2) \n \text{radius}=(4)/(2) \n \text{radius}=2 \end{gathered}$

Then,

Volume of the sphere is given by:

$\begin{gathered} (4)/(3)*\pi* r^3=(4)/(3)*3.14*2^3 \n =(4)/(3)*3.14*8 \n =33.5 \end{gathered}$

And,

The volume of a cube is:

$\begin{gathered} \text{Volume of cube=side}* side* side \n =4*4*4 \n =64\text{ inches} \end{gathered}$

Then,

The volume of the space between the sphere and cube = 64-33.5 = 30.5.

Hence, the answer is 30.5 cube inches.

In? gambling, the chances of winning are often written in terms of odds rather than probabilities. The odds of winning is the ratio of the number of successful outcomes to the number of unsuccessful outcomes. The odds of losing is the ratio of the number of unsuccessful outcomes to the number of successful outcomes. For? example, if the number of successful outcomes is 2 and the number of unsuccessful outcomes is? 3, the odds of winning are 2:3(Note; if the odds of winning are 2/3, the propability of sucess is2/5)The odds of event occuring are 1:6. Find (a) the propability that the event will occur,(b) propability that the event will not occur.

(a)The propability that event will occur is....(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED.)

(b)The propability thet the event will not occur is...(TYPE AN INTEGER OR DECIMAL ROUNDED TO THE NEAREST THOUSANDTH AS NEEDED)

Answers

Answer:

A) The probability that the event will occur $=(1)/(7)$

B)The probability that the event will not occur = $(6)/(7)$

Step-by-step explanation:

We are given that The odds of event occurring are 1:6.

So, Number of successful events = 1

Number of unsuccessful events = 6

So, Total events = 6+1=7

a)the probability that the event will occur= $\frac{\text{Favorable event}}{\text{Total event}}$

The probability that the event will occur $=(1)/(7)$

b)The probability that the event will not occur = $\frac{\text{Favorable event}}{\text{Total event}}$

The probability that the event will not occur = $(6)/(7)$

What'd the greatest common factor (GCF) for each pair of numbers. 25, 55 The GCE IS

Answers

Answer:

Step-by-step explanation:

5 l 25,55

l 5,11

NO LINKS OR ANSWERING WHAT YOU DON'T KNOW?1. Suppose y varies inversely with x, and y = 25 when x = 1/5. What is the value of y when x = 5?

a. 15
b. 5
c. 25
d. 1

2. Suppose y varies inversely with x, and y = a when x = a^2. What inverse variation equation related x and y?

a. y = a^2/x
b. y = a^3/x
c. y= a^3x
d. y = ax

3. Suppose y varies inversely with x, and y = 3 when x = 1/3. What is the inverse variation equation that relates x and y?

a. y = 1/x
b. y =x
c. y = 3x
d. y = 3/x

Answers

Answer:

1. D. 1

2. B. y=a³/x

3. A. y=1/x

Step-by-step explanation:

too long to give te explanations but they're there in the attachments

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