Ask question

Ask question

All categories

3 years ago

5

A student ran out of time on a multiple choice exam and randomly guessed the answers for two problems. Each problem had 5 answer

choices - a, b, c, d, e- and only one correct answer. What is the probability that she answered neither of the problems correctly? Do not round your answer. (If necessary, consult a list of formulas.)

1 answer:

choli [55]3 years ago

3 0

Answer:

there is a 64% chance that the student got both problems wrong

a 32% chance that they got only 1 correct

and a 4% chance that they got both correct

Step-by-step explanation:

There are 25 total possible combinations of answers, with 8 possible combinations where the student would get 1 answer right, and 1 combination where the student would get both answers correct.

$25-9=16$

$\frac{16}{25} =\frac{x}{100}$

$\frac{64}{100}$

$64$ %

$\frac{8}{25} =\frac{y}{100}$

$\frac{32}{100}$

$32$ %

$\frac{1}{25} =\frac{z}{100}$

$\frac{4}{100}$

$4$ %

You might be interested in

Fill in the blank. principal: $300 Rate: 3% Time: 4 years Interest Earned: ? New Balance: ?

Wittaler [7]

Answer:

300x.03 all divided by 4

Step-by-step explanation:

7 0

2 years ago

Can you please help this is urgent??!!!!

Thepotemich [5.8K]

Answer:

B. 4

Step-by-step explanation:

A direct proportion has the form

y = kx or k=y/x,

where k is the proportionality constant.

Let's test some points.

Second point

k = 8/2 = 4

Fifth point

k = 23/5.75 = 4

You will get the same result for every point, so the constant of proportionality is 4.

3 0

3 years ago

Rachel has 90p. Simon has £2.

natulia [17]

Answer:

9:20 is the answers for the question

Step-by-step explanation:

please tell me your

6 0

2 years ago

Read 2 more answers

Two equations are given below:

ch4aika [34]

Rewrite the equations;
m+4n=8
m-n=-2

Eliminating m gives;
5n=10
n=2
Replacing for n in the first equation;
m+4(2)=8
m=8
Answer;
(0, 2)

6 0

3 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

$Z = \frac{X - \mu}{s}$

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

$Z = \frac{X - \mu}{s}$

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

$Z = \frac{X - \mu}{s}$

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

$Z = \frac{X - \mu}{\sigma}$

By the Central Limit Theorem

$Z = \frac{X - \mu}{s}$

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

$Z = \frac{X - \mu}{s}$

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

5 0

3 years ago