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Tcecarenko [31]
2 years ago
5

The time for a professor to grade an exam is normally distributed with a mean of 16.3 minutes and a standard deviation of 4.2 mi

nutes.
What is the probability that a randomly selected exam will require between 14 and 19 minutes to​ grade?

A.0.4477

B.0.3175

C.0.3804

D.0.5837
Mathematics
1 answer:
dangina [55]2 years ago
7 0

Answer:

A.0.4477

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 = 16.3, \sigma = 4.2

What is the probability that a randomly selected exam will require between 14 and 19 minutes to​ grade?

This probability is the pvalue of Z when X = 19 subtracted by the pvalue of Z when X = 14. So

X = 19

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

Z = \frac{19 - 16.3}{4.2}

Z = 0.64

Z = 0.64 has a pvalue of 0.7389.

X = 14

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

Z = \frac{14 - 16.3}{4.2}

Z = -0.55

Z = -0.55 has a pvalue of 0.2912

0.7389 - 0.2912 = 0.4477

So the correct answer is:

A.0.4477

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Answer:

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Step-by-step explanation:

(0,-7) is the y-intercept

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m is the slope

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plug it in:

y=3/4x-7

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Answer:

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Step-by-step explanation:

It would be 3 hours because after three hours, the candle that can only burn for 3 hours will have burned out. This leaves the candles that can burn for 4 and 5 hours. I guess if you want to get really specific you could say 3 hours and 59 minutes but I'm not totally sure how your teacher wants the answer

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An aeroplane takes 4 hours to travel a distance of 440 0km. Another aeroplane travels at a speed which is 100km per hour less th
FrozenT [24]

Answer:

7480 hours

Step-by-step explanation:

440 - 100 = 340

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440 = 2 × 2 × 2 × 5 × 11

340 = 2 × 2 × 5 × 17

LCM = 2 × 2 × 2 × 5 × 11 × 17

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Please solve 2x+1<1 or x+5>8 for me please xx <3​
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Answer:

x=0

Step-by-step explanation:

Subtract 1 from both sides

2x+1-1<1-1

Simplify the arithmetic

2x<1-1

Simplify the arithmetic

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The amount of time that people spend at Grover Hot Springs Spa is normally distributed with a mean of 63 minutes and a standard
PtichkaEL [24]

Answer:

a)X \sim N(63,18)  

Where \mu=63 and \sigma=18

b) P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>1.5)=1-P(Z

c) P(X

P(Z

d) P(60

P(-0.167

P(-0.167

e)  IQR = 75.13-50.87=24.26

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Part a

Let X the random variable that represent the amount of time that people spend at Grover Hot Springs of a population, and for this case we know the distribution for X is given by:

X \sim N(63,18)  

Where \mu=63 and \sigma=18

Part b

We are interested on this probability

P(X>90)

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X>90)=P(\frac{X-\mu}{\sigma}>\frac{90-\mu}{\sigma})=P(Z>\frac{90-63}{18})=P(Z>1.5)

And we can find this probability using the complement rule and with the normal standard table or excel:

P(Z>1.5)=1-P(Z

Part c

We are interested on this probability

P(X

And the best way to solve this problem is using the normal standard distribution and the z score given by:

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

If we apply this formula to our probability we got this:

P(X

And we can find this probability using the normal standard table or excel:

P(Z

Part d

If we apply this formula to our probability we got this:

P(60

And we can find this probability with this difference:

P(-0.167

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.  

P(-0.167

Part e

Q1

For this part we want to find a value a, such that we satisfy this condition:

P(X>a)=0.75   (a)

P(X   (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.  

As we can see on the figure attached the z value that satisfy the condition with 0.25 of the area on the left and 0.75 of the area on the right it's z=-0.674. On this case P(Z<-0.674)=0.25 and P(z>-0.674)=0.75

If we use condition (b) from previous we have this:

P(X  

P(z

But we know which value of z satisfy the previous equation so then we can do this:

z=-0.674

And if we solve for a we got

a=63 -0.674*18=50.87

So the value of height that separates the bottom 25% of data from the top 75% is 50.87.  

Q3

Since the distribution is symmetrical we repaeat the procedure for Q1 but now with z= 0.674

z=0.674

And if we solve for a we got

a=63 +0.674*18=75.13

And then the IQR = 75.13-50.87=24.26

3 0
2 years ago
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