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2 years ago

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

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 $z\approx0.4399$ .

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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 = numbers of seals observed

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 = 0.0516

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 a rectangular prism =B*h------> equation 1
where
B is the area of the base
h is the height

volume of a rectangular pyramid=(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 rectangular pyramid=(1/3)*volume of a rectangular prism

the answer part a) is
volume of a rectangular pyramid=(1/3)*volume of a rectangular prism

Part b) If the pyramid was full of water, how much of the prism would it fill up?

the answer part b) is
If the pyramid was filled with water, the prism would only fill 1/3 of its volume

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

cones and cylinders

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

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