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Mila [183]
3 years ago
5

Just need help with #6

Mathematics
1 answer:
Anarel [89]3 years ago
3 0

Answer:

Step-by-step explanation:

a) The rate of change is referred to as slope

Slope = change in value of y on the vertical axis / change in value of x on the horizontal axis

change in the value of y = y2 - y1

Change in value of x = x2 -x1

From the graph,

y2 = 160 = final value of y

y 1 = 260 = initial value of y

x2 = 10 = final value of x

x1 = 5 = initial value of x.

Slope = (160 - 260)/10 - 5)=-100/5

Slope = -20

b) initial height of the biker above the Canyon was 360 feets. It is reducing as the time is increasing.

c) it took the hiker 18 minutes to reach the Canyon floor.

d) After 9 minutes, the hiker was 180 feets above the Canyon floor

e) it took 7 minutes for the hiker to reach 220 feets above the Canyon floor.

f) The domain is the set of all possible values of the independent variable and the independent variable is time.

The time between which the hiker was at the maximum height and the minimum height lies between 18 minutes and 0 minutes.

The domain is 0 lesser than or equal to t lesser than or equal to 18.

The range is the set of all possible values of the dependent variable and the dependent variable is height of the hiker above the Canyon. The maximum height of the hiker was 360 feet and the minimum height of the hiker was 0 feet. Let the height be h.

The range is 0 lesser than or equal to h lesser than or equal to 360

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Answer:

a) P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

b) P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

c) P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

Step-by-step explanation:

1) Previous concepts

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

2) Solution to the problem

Let X the random variable of interest, on this case we now that:

X \sim Binom(n=10, p=0.32)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

Part a

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

Part b

P(X> 2)=1-P(X\leq 2)=1-[P(X=0)+P(X=1)+P(X=2)]

P(X=0)=(10C0)(0.32)^0 (1-0.32)^{10-0}=0.0211  

P(X=1)=(10C1)(0.32)^1 (1-0.32)^{10-1}=0.0995

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X> 2)=1-P(X\leq 2)=1-[0.0211+0.0995+0.211]=0.668

Part c

P(2 \leq x \leq 5)=P(X=2)+P(X=3)+P(X=4)+P(X=5)

P(X=2)=(10C2)(0.32)^2 (1-0.32)^{10-2}=0.211

P(X=3)=(10C3)(0.32)^3 (1-0.32)^{10-3}=0.264

P(X=4)=(10C4)(0.32)^4 (1-0.32)^{10-4}=0.218

P(X=5)=(10C5)(0.32)^5 (1-0.32)^{10-5}=0.123

P(2 \leq x \leq 5)=0.211+0.264+0.218+0.123=0.816

6 0
3 years ago
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