Mathematics, 26.02.2020 17:52 kiasiab17

A statistics practitioner determined that the mean and stan-dard deviation of a data set were 90 and 15, respectively. What can yousay about the proportions of observations that lie between each of thefollowing intervals if you know that the distribution is bell-shaped? Whatcan you say if the distribution is not bell-shaped?

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Answer from: erykp17

If the distribution is bell shaped we can approximate the probability with high accuracy using the z score formula.

a) P(75

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(75

b) P(60

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(60

c) P(45

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(45

If the distribution is NOT bell shaped the approximation with the z score NOT works and we need to have the distribution for X in order to find the probabilities.

Step-by-step explanation:

Previous concepts

If the distribution is bell shaped we can approximate the probability with high accuracy using the z score formula.

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable of interest

We assume for this case that $\mu=90$ and $\sigma=15$

We are interested on this probability

P(75

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(75

Part b

P(60

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(60

Part c

P(45

And for this case we can use the z score given by:

$z = \frac{X-\mu}{\sigma}$

And if we use it we got:

P(45

If the distribution is NOT bell shaped the approximation with the z score NOT works and we need to have the distribution for X in order to find the probabilities.

Answer from: Quest

yo answer should be 6 if im not mistaken

step-by-step explanation:

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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A statistics practitioner determined that the mean and stan-dard deviation of a data set were 90 and...