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Readme [11.4K]
3 years ago
7

The time spent waiting in the line is approximately normally distributed. The mean waiting time is 6 minutes and the variance of

the waiting time is 4.
Find the probability that a person will wait for more than 7 minutes. Round your answer to four decimal places.
Mathematics
1 answer:
White raven [17]3 years ago
7 0

Answer:

0.3075 = 30.75% probability that a person will wait for more than 7 minutes.

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.

The standard deviation is the square root of the variance.

In this problem, we have that:

\mu = 6, \sigma = \sqrt{4} = 2

Find the probability that a person will wait for more than 7 minutes.

This is 1 subtracted by the pvalue of Z when X = 7. So

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

Z = \frac{7 - 6}{2}

Z = 0.5

Z = 0.5 has a pvalue of 0.6915

1 - 0.6915 = 0.3075

0.3075 = 30.75% probability that a person will wait for more than 7 minutes.

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muminat
Factors are what is being multiplied or divided. In this problem, you have 6 times X times Y. So, you have 3 factors. 
6 0
3 years ago
Find n.<br> 12/18=n/36<br> n=_____
Vaselesa [24]
18 x 2 = 36
n = 12 x 2
n = 24
3 0
3 years ago
A rock is dropped from a bridge 320 feet above the river. The pathway that the rock takes can be modeled by the equation h= -16t
Marina86 [1]

Answer:

The rock will take about 4.5 seconds to reach the river

Step-by-step explanation:

* lets study the situation of the rock

- The rock is dropped means the initial velocity is zero

- The motion is free fall under earth gravity

- The rock dropped from a bridge 320 feet above the river

- The equation of the pathway is h = -16t² + 320

- When the rock reach to the ground the height will be zero

* Now lets substitute h by zero in the equation to find t

∵ h = -16t² + 320

∵ h = 0

∴ 0 = -16t² + 320 ⇒ add 16t² to both sides

∴ 16t² = 320 ⇒ divide both sides by 16

∴ t² = 320/16 = 20

∴ t² = 20 ⇒ take √ for both sides

∴ t = √20 = 2√5 ≅ 4.5 seconds

* The rock will take about 4.5 seconds to reach the river

4 0
3 years ago
Solve the equation for y.<br><br> 6y+x=8
iVinArrow [24]

Answer:

The correct answer is \bold{y = -\frac{1}{6}x+\frac{4}{3}}.

Step-by-step explanation:

We want to solve for y in the given equation. We can do this by rearranging the equation and using operational techniques to simplify.

6y + x = 8 \ $\tex Subtract x from both sides of the equation.

6y + x - x = 8 - x \ $\tex Carry out the operation.

6y = 8 - x \ $\tex Rearrange so the equation lists the variables first and the constants second.

6y = -x + 8 \ $\tex Create a coefficient for the x-variable (this is -1).

6y = -1x + 8 \ $\tex Divide by 6 on both sides of the equation in order to isolate the y-variable.

\frac{6y}{6}=\frac{-1x}{6} + \frac{8}{6} \ $\tex Carry out this operation by simplifying the fractions and dividing out the operations accordingly.

y = -\frac{1}{6}x+\frac{4}{3} \ $\tex Be sure to verify that all fractions and terms are simplified as far as they can be and that the equation is written in proper syntax.

Because we have the <em>y</em>-variable isolated from the rest of the equation, we are done!

6 0
2 years ago
A number cube was rolled as part of an experiment. The results are displayed in the table below. Number 1 2 3 4 5 6 Frequency 4
Neporo4naja [7]

Answer:

the answer is C

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Step-by-step explanation:

7 1
3 years ago
Read 3 more answers
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