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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answered: 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.

answered: Guest

the number of possible outcomes that do not show a 1 on the first spinner and show the number 4 on the second spinner is 2.

spinner 1 spinner 2

1 1

1 2

1 3

1 4

2 1

2 2

2 3

2 4 = not 1, and 4

3 1