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mylen [45]
2 years ago
10

In a standard normal distribution, what z value corresponds to 17% of the data between the mean and the z value?

Mathematics
1 answer:
hjlf2 years ago
4 0
You're looking for a value z such that

\mathbb P(0

Because the distribution is symmetric, the value of z in either case will be the same.

Now, because the distribution is continuous, you have that

0.17=\mathbb P(0

The mean for the standard normal distribution is 0, and because the distribution is symmetric about its mean, it follows that \mathbb P(Z.

0.17=\mathbb P(Z

You can consult a z score table to find the corresponding score for this probability. It turns out to be z\approx0.4399.
You might be interested in
At a certain airport, 75% of the flights arrive on time. A sample of 10 flights is studied. Assume each flight is independent of
mars1129 [50]

Answer:

52.56% probability that eight or more of the flights will arrive on time.

Step-by-step explanation:

For each flight, there are only two possible outcomes. Either it is on time, or it is not. The probability of a flight being on time is independent from other flights. So we use the binomial probability distribution to solve this question.]

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

In which C_{n,x} is the number of different combinations of x objects from a set of n elements, given by the following formula.

C_{n,x} = \frac{n!}{x!(n-x)!}

And p is the probability of X happening.

At a certain airport, 75% of the flights arrive on time.

This means that p = 0.75

A sample of 10 flights is studied.

This means that n = 10

Find the probability that eight or more of the flights will arrive on time.

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10)

In which

P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}

P(X = 8) = C_{10,8}.(0.75)^{8}.(0.25)^{2} = 0.2816

P(X = 9) = C_{10,9}.(0.75)^{9}.(0.25)^{1} = 0.1877

P(X = 10) = C_{10,10}.(0.75)^{10}.(0.25)^{0} = 0.0563

P(X \geq 8) = P(X = 8) + P(X = 9) + P(X = 10) = 0.2816 + 0.1877 + 0.0563 = 0.5256

52.56% probability that eight or more of the flights will arrive on time.

4 0
2 years ago
Read 2 more answers
PROBLEM SOLVING Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during
Akimi4 [234]

Answer:

Probability that at most 50 seals were observed during a randomly chosen survey is 0.0516.

Step-by-step explanation:

We are given that Scientists conducted aerial surveys of a seal sanctuary and recorded the number x of seals they observed during each  survey.

The numbers of seals observed were normally distributed with a mean of 73 seals and a standard deviation of 14.1 seals.

Let X = <u><em>numbers of seals observed</em></u>

The z score probability distribution for normal distribution is given by;

                             Z  =  \frac{X-\mu}{\sigma}  ~ N(0,1)

where, \mu = population mean numbers of seals = 73

            \sigma = standard deviation = 14.1

Now, the probability that at most 50 seals were observed during a randomly chosen survey is given by = P(X \leq 50 seals)

            P(X \leq 50) = P( \frac{X-\mu}{\sigma} \leq \frac{50-73}{14.1} ) = P(Z \leq -1.63) = 1 - P(Z < 1.63)    

                                                          = 1 - 0.94845 = <u>0.0516</u>

The above probability is calculated by looking at the value of x = 1.63 in the z table which has an area of 0.94845.

4 0
2 years ago
The volume, V, of a rectangular prism is determined using the formula V=lwh, where l is the length, w is the width, and h is the
Olegator [25]

Answer:

Width of the rectangular prism

It is given to us that the volume of the rectangular prism is calculated by the given formula :-

v = lwh

Where,

v = volume

l = length

w = width

h = height

Now,

In the question we are given :-

v = 138.24 cubic inches

h =  9.6 inches

l = 3.2 inches

w = ?

Substitute these values in the volume formula given :-

138.24 = 3.2 * w * 9.6

138.24 = 30.72 * w

w = 138.24/30.72

w = 4.5

⇒ The width of the rectangular prism is 4.5 inches.

9 2
2 years ago
Read 4 more answers
If a random variable X is exponentially distributed with parameter λ=2, then P(X≥1) is equal to
Rasek [7]

Answer:

D. 0.1353

B. 0.0473

Step-by-step explanation:

For an exponentially distributed random variable, the cumulative distribution function is:

P(x\leq a) = 1 - e^{-\lambda a}\\P(x\geq a) = e^{-\lambda a}

with parameter λ=2, then P(X≥1) is equal to:

P(x\geq 1) = e^{-2*1}=0.1353

D. 0.1353

with parameter λ=1.5, then P(2≤X≤4) is equal to

P(2\leq x \leq 4) = P(x \leq 4) - P(x\leq 2)\\P(2\leq x \leq 4) =1 - (e^{-1.5*4}) - (1-(e^{-1.5*2}))\\P(2\leq x \leq 4) = 0.0473

B. 0.0473

7 0
2 years ago
Given a rectangular pyramid and a rectangular prism that have the same base and same height, how do their volumes compare? If th
Luden [163]
We know that
volume of <span>a rectangular prism =B*h------> equation 1
where
B is the area of the base
h is the height 

volume of </span><span>a rectangular pyramid=(1/3)*B*h-----> equation 2
where
</span>B is the area of the base
h is the height 
<span>
substitute equation 1 in equation 2
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
the answer part a) is
</span>volume of a rectangular pyramid=(1/3)*volume of a rectangular prism
<span>
Part b) </span><span>If the pyramid was full of water, how much of the prism would it fill up?
</span>
the answer part b) is
<span>If the pyramid was filled with water, the prism would only fill 1/3 of its volume

Part c) </span><span>Name another pair of three-dimensional objects that have a relationship similar to this

cones and cylinders

</span>volume of a cylinder =B*h------> equation 1
where
B is the area of the base
h is the height <span>

</span>volume of a cone=(1/3)*B*h-----> equation 2
where
B is the area of the base
h is the height 

substitute equation 1 in equation 2
volume of a cone=(1/3)*volume of a cylinder
4 0
2 years ago
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