What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2

The time for a professor to grade a student's homework in statistics is normally distributed with a mean of 12.6 minutes and a s

Rus_ich [418]

Answer:

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

Step-by-step explanation:

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.

In this problem, we have that:

$\mu = 12.6, \sigma = 2.5$

What is the probability that randomly selected homework will require between 8 and 12 minutes to grade?

This is the pvalue of Z when X = 12 subtracted by the pvalue of Z when X = 8. So

X = 12

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

$Z = \frac{12 - 12.6}{2.5}$

$Z = -0.24$

$Z = -0.24$ has a pvalue of 0.4052

X = 8

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

$Z = \frac{8 - 12.6}{2.5}$

$Z = -1.84$

$Z = -1.84$ has a pvalue of 0.0329

0.4052 - 0.0329 = 0.3723

37.23% probability that randomly selected homework will require between 8 and 12 minutes to grade

7 0

2 years ago

A six-sided fair die is rolled and a fair coin is tossed. If event M represents getting an odd number on the die and event N rep

poizon [28]

Answer:

The two events are independent. In the given scenario, P(M and N) =0.25

Explanation:

1) Independent events are those that do not affect each other. In this case the number that you roll does not change the flip of the coin. So, whatever number you get with the die, the probabilities of landing tail or head when tossing the coin are the same.

2) The probability of the two simultaneous events: getting an odd number and landing a tail, since they are independent, is equal to the product of the two independent events:
P(M and N) = P(M) x P (N) (only because they are independent)

3) The probability of getting and odd number is 0.5 (half of the numbers are odd and half are even => probability = 1/2)

4) The probability of the coin lands tail is 0.5 (1/2).

5) Then the joint probability is 0.5 x 0.5 = 0.25

3 0

2 years ago

A museum employee surveys a random sample of 350 visitors to the museum. If those visitors, 266 stopped at the gift shop. Based

Free_Kalibri [48]

Answer:

about 2432 people(well exactly this many are supposed to go)

Step-by-step explanation:

266 visitors out of 350 means 19/25 people go to the gift shop. now we multiply this by 3200 to get the number of people who would go to get 2432

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8 0

2 years ago

Read 2 more answers

If AY parallel to CX, then find ∠ABC please help!!!!!!!!!!!!!!!!!!!

romanna [79]

Answer:

60°

Step-by-step explanation:

Through point B draw a line m || AY || CX and take two points say E and F on left and right side of point B respectively.

Therefore,

m∠FBC + m∠XCB = 180°..(By interior angle property)

m∠FBC + 130° = 180°

m∠FBC = 180° - 130°

m∠FBC = 50°....(1)

Next,

m∠ABF = m∠BAY... (Alternate angles)

m∠ABC + m∠FBC = 110°

(since, m∠ABF = m∠ABC + m∠FBC)

m∠ABC + 50° = 110° (From equation 1)

m∠ABC = 110° - 50°

$\huge \purple {\boxed {m\angle ABC = 60\degree}}$

8 0

2 years ago

This figure shows circle O with chords PM and LN .

emmainna [20.7K]

A circle with two minor arcs equal in measure.
So LN=PM

5 0

2 years ago

Read 2 more answers

What is the quotient (2x4 – 3x3 – 3x2 + 7x – 3) ÷ (x2 – 2x + 1)?