Find the proportion. <br> Test is worth 50 points; test score of 84%

An Airliner has a capacity for 300 passengers. If the company overbook a flight with 320 passengers, What is the probability tha

TEA [102]

Answer:

The probability is $P(X >300 ) = 0.97219$

Step-by-step explanation:

From the question we are told that

The capacity of an Airliner is k = 300 passengers

The sample size n = 320 passengers

The probability the a randomly selected passenger shows up on to the airport

$p = 0.96$

Generally the mean is mathematically represented as

$\mu = n* p$

=> $\mu = 320 * 0.96$

=> $\mu = 307.2$

Generally the standard deviation is

$\sigma = \sqrt{n * p * (1 -p ) }$

=> $\sigma = \sqrt{320 * 0.96 * (1 -0.96 ) }$

=> $\sigma =3.50$

Applying Normal approximation of binomial distribution

Generally the probability that there will not be enough seats to accommodate all passengers is mathematically represented as

$P(X > k ) = P( \frac{ X -\mu }{\sigma } > \frac{k - \mu}{\sigma } )$

Here $\frac{ X -\mu }{\sigma } =Z (The \ standardized \ value \ of \ X )$

=> $P(X >300 ) = P(Z > \frac{300 - 307.2}{3.50} )$

Now applying continuity correction we have

$P(X >300 ) = P(Z > \frac{[300+0.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > \frac{[300.5] - 307.2}{3.50} )$

=> $P(X >300 ) = P(Z > -1.914 )$

From the z-table

$P(Z > -1.914 ) = 0.97219$

So

$P(X >300 ) = 0.97219$

8 0

3 years ago

I need help with these two answers please :/

4vir4ik [10]

Rise over run is -2/4 or simplified as -1/2
The second one is
$\frac{1 - 3}{4 - 0} = \frac{ - 2}{4}$

7 0

3 years ago

What is the area of this trapezoid? { Please answer ASAP , I need it now! }. A= h(b1+b2) then divide by 2

OlgaM077 [116]

Answer:

30in squared

Step-by-step explanation:

(4x5) + ((4x3)/2) + ((4x2)/2) = 20 in sq.

6 0

3 years ago

A sample of blood pressure measurements is taken for a group of adults, and those values (mm Hg) are listed below. The values

Slav-nsk [51]

Answer:

Systolic on right

$\hat{CV} =\frac{18.68}{127.5}=0.147$

Systolic on left

$\hat{CV} =\frac{12.65}{74.2}=0.170$

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.

Step-by-step explanation:

Assuming the following data:

Systolic (#'s on right) Diastolic (#'s on left)

117; 80

126; 77

158; 76

96; 51

157; 90

122; 89

116; 60

134; 64

127; 72

122; 83

The coefficient of variation is defined as " a statistical measure of the dispersion of data points in a data series around the mean" and is defined as:

$CV= \frac{\sigma}{\mu}$

And the best estimator is $\hat {CV} =\frac{s}{\bar x}$

Systolic on right

We can calculate the mean and deviation with the following formulas:

[te]\bar x = \frac{\sum_{i=1}^n X_i}{n}[/tex]

$s= \frac{\sum_{i=1}^n (x_i -\bar X)^2}{n-1}$

For this case we have the following values:

$\bar x = 127.5, s= 18.68$

So then the coeffcient of variation is given by:

$\hat{CV} =\frac{18.68}{127.5}=0.147$

Systolic on left

For this case we have the following values:

$\bar x = 74.2 s= 12.65$

So then the coeffcient of variation is given by:

$\hat{CV} =\frac{12.65}{74.2}=0.170$

So for this case we have more variation for the data of systolic on left compared to the data systolic on right but the difference is not big since 0.170-0.147 = 0.023.

4 0

2 years ago

Which expression is equivalent to 7a^3(6a^2+a^2)-4a^6?

Thepotemich [5.8K]

Simply simplify:

7a³(7a²)-4a^6 ⇒ 49a^6 - 4a^6 ⇒ 45a^6

Hope that helps!

3 0

3 years ago

Find the proportion. Test is worth 50 points; test score of 84%