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kotegsom [21]
2 years ago
8

Consider the probability that greater than 99 out of 158 flights will be on-time. Assume the probability that a given flight wil

l be on-time is 64%. Approximate the probability using the normal distribution. Round your answer to four decimal places
Mathematics
1 answer:
Nikitich [7]2 years ago
8 0

Answer:0.1514

Step-by-step explanation:

Let n be the no of flights on time =145

Let  p be the probability that a flight be on time=0.64

Check the condition for normal approximation to the binomial distribution

np\geq 10

92.8\geq 10

Also

n(1-p)\geq 10

52.2\geq 10

Both the conditions satisfied ,so the normal distribution can be used to approximate probability

mean\mu =92.8

Standard deviation\left ( \sigma \right )=\sqrt{np\left ( 1-p\right )}

\sigma =5.779

P\left ( X>99\right )=1-P\left ( x\leqslant 99\right )

P\left ( X>99\right )=1-P\left ( \frac{x-\mu }{\sigma }\leq \frac{99-92.8}{5.779}\right )

P\left ( X>99\right )=1-P\left [ 1.072\right ]

P=1-08485\approx 0.1514

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A new sample of 225 employed adults is chosen. Find the probability that less than 7.1% of the individuals in this sample hold m
arsen [322]

Answer:

The probability that less than 7.1% of the individuals in this sample hold multiple jobs is 0.0043.

Step-by-step explanation:

Let <em>X</em> = number of individuals in the United States who held multiple jobs.

The probability that an individual holds multiple jobs is, <em>p</em> = 0.13.

The sample of employed individuals selected is of size, <em>n</em> = 225.

An individual holding multiple jobs is independent of the others.

The random variable <em>X</em> follows a Binomial distribution with parameters <em>n</em> = 225 and <em>p</em> = 0.13.

But since the sample size is too large Normal approximation to Binomial can be used to define the distribution of proportion <em>p</em>.

Conditions of Normal approximation to Binomial are:

  • np ≥ 10
  • n (1 - p) ≥ 10

Check the conditions as follows:

np=225\times 0.13=29.25>10\\n(1-p)=225\times (1-0.13)=195.75>10

The distribution of the proportion of individuals who hold multiple jobs is,

p\sim N(p, \frac{p(1-p)}{n})

Compute the probability that less than 7.1% of the individuals in this sample hold multiple jobs as follows:

P(p

*Use a <em>z</em>-table.

Thus, the probability that less than 7.1% of the individuals in this sample hold multiple jobs is 0.0043.

7 0
3 years ago
Write an equation of a line in point-slope form that has a slope of -2 and passes through (5, -1).
gavmur [86]

Answer:

y+1=-2(x-5)

Step-by-step explanation:

We can write the equation of a line in 3 different forms including slope intercept, point-slope, and standard depending on the information we have. We have a point given and a slope from the equation. We will chose point-slope since we have a point and the slope.  

We will substitute m=-2 and x_1=5\\y_1=-1.

y-(-1)=-2 (x-5)

y+1=-2(x-5)

This is the equation of the line with slope -2 that passes through (5,-1).


8 0
3 years ago
Point A is at (6,-6) and point C is at(-6,-2). find the coordinates of B on AC so that AB= 3/4AC.
loris [4]

Answer:

B(-6, 0)

Step-by-step explanation:

You want to find B such that ...

(B -A) = (3/4)(C -A) . . . . the required distance relation

4(B -A) = 3(C -A) . . . . . . multiply by 4

4B = 3C +A . . . . . . . . . . add 4A, simplify

Now, we can solve for B and substitute the given coordinates:

B = (3C +A)/4 = (3(-6, -2) +(-6, 6))/4 = (-24, 0)/4 = (-6, 0)

The coordinates of point B are (-6, 0).

Hope it helped u if yes mark me BRAINLIEST!

Tysm!

:D

6 0
3 years ago
Emma has saved £1.35 in 5p coins. How many 5p coins does Emma have?
KengaRu [80]


imagine 135/5

which = 27

Emma has 27 of her 5 pence coins

3 0
3 years ago
Read 2 more answers
Find the value of A<br> A: 18<br> B: 21<br> C: 20<br> D: 17
AnnZ [28]

These are vertical angles so they are equal so

6a +  11  = 2a + 83  

now solve for a

6 0
3 years ago
Read 2 more answers
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