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MAXImum [283]
3 years ago
14

The amount of time a passenger waits at an airport check-in counter is random variable with mean 10 minutes and standard deviati

on of 2 minutes. Suppose a random sample of 50 customers is observed. Calculate the probability that the average waiting time waiting in line for this sample is (a) less than 10 minutes (b) between 5 and 10 minutes
Mathematics
1 answer:
Stolb23 [73]3 years ago
3 0

Answer:

(a) less than 10 minutes

= 0.5

(b) between 5 and 10 minutes

= 0.5

Step-by-step explanation:

We solve the above question using z score formula. We given a random number of samples, z score formula :

z-score is z = (x-μ)/ Standard error where

x is the raw score

μ is the population mean

Standard error : σ/√n

σ is the population standard deviation

n = number of samples

(a) less than 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Therefore, the probability that the average waiting time waiting in line for this sample is less than 10 minutes = 0.5

(b) between 5 and 10 minutes

i) For 5 minutes

x = 5 μ = 10, σ = 2 n = 50

z = 5 - 10/2/√50

z = -5 / 0.2828427125

= -17.67767

P-value from Z-Table:

P(x<5) = 0

Using the z table to find the probability

P(z ≤ 0) = P(z = -17.67767) = P(x = 5)

= 0

ii) For 10 minutes

x = 10 μ = 10, σ = 2 n = 50

z = 10 - 10/2/√50

z = 0 / 0.2828427125

z = 0

Using the z table to find the probability

P(z ≤ 0) = P(z < 0) = P(x = 10)

= 0.5

Hence, the probability that the average waiting time waiting in line for this sample is between 5 and 10 minutes is

P(x = 10) - P(x = 5)

= 0.5 - 0

= 0.5

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Step-by-step explanation:

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2 years ago
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Answer: It will take Jane 14 days to run 41 miles

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41-6= 35
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A circle has a diameter with endpoints at (6, 5) and (8, 5). Write the equation for the circle.
mario62 [17]

Answer:

(x-7)^2+(y-5)^2=1

Step-by-step explanation:

The two things that are required to formulate the equation of the circle is the center coordinate and the radius of the circle!

<u>Center of the circle:</u>

  • The center of the circle always lies at the midpoint of the endpoints of its diameter: Let's call the endpoints A(6,5) and B(8,5).

Using the midpoint formula we'll get:

(x_m, y_m) = \left(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\right)

(x_m, y_m) = \left(\dfrac{6+8}{2},\dfrac{5+5}{2}\right)

(x_m, y_m) = (7,5)

This is the center coordinate of our circle.

<u>Radius: </u>

The radius of the circle is the distance from the center of the circle to any of the endpoints of the diameter (A or B)

We can use the distance formula:

r = \sqrt{(x_1-x_2)^2+(y_1-y_2)^2}

r = \sqrt{(x_1-x_m)^2+(y_1-y_m)^2}

r = \sqrt{(6-7)^2+(5-5)^2}

r = \sqrt{1^2}

r = 1

<u>Equation of the circle: </u>

The equation is written as:

(x-a)^2+(y-b)^2=r^2

here, (a,b) are the center points of the circle

in our case this is (a,b)=(x_m,y_m)=(7,5)

and r = 1

(x-7)^2+(y-5)^2=1^2

(x-7)^2+(y-5)^2=1

This is the equation of the circle!

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