Which describes lines that have exactly one point in common? parallel lines intersecting lines skew lines line segments

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11. Use the TI-84 Plus calculator. (a) I

sukhopar [10]

Answer:

a) We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

b) There is a 15.97% probability that x will be between 54 and 55.

c) The 47th percentile of x is $X = 52.877$ .

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by

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

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

A sample of size 45 will be drawn from a population with mean 53 and standard deviation 11.

This means that $\mu = 53$ .

We have to find the standard deviation of the sample, that is:

$\sigma = \frac{11}{\sqrt{45}} = 1.64$

(a) Is it appropriate to use the normal distribution to find probabilities for x?

We have the standard deviation and the mean, so it is appropriate to use the normal distribution to find probabilities for x.

(b) Find the probability that x will be between 54 and 55.

This is the pvalue of the Z score when X = 55 subtracted by the pvalue of the Z score when X = 54.

X = 55

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

$Z = \frac{55 - 53}{1.64}$

$Z = 1.22$

$Z = 1.22$ has a pvalue of 0.88877.

X = 54

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

$Z = \frac{54 - 53}{1.64}$

$Z = 0.61$

$Z = 0.61$ has a pvalue of 0.72907.

So, there is a 0.88877 - 0.72907 = 0.1597 = 15.97% probability that x will be between 54 and 55.

(c) Find the 47th percentile of x. Round the answer to at least two decimal places.

This is the value of X when Z has a pvalue of 0.47;

This is between $Z = -0.07$ and $Z = -0.08$ . So we use $Z = -0.075$ .

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

$-0.075 = \frac{X - 53}{1.64}$

$X = 52.877$

The 47th percentile of x is $X = 52.877$ .

8 0

3 years ago

PART 3 OF ME ASKING FOR HELP

e-lub [12.9K]

Answer:

c

Step-by-step explanation:

7 0

3 years ago

What is the absolute deviation for 62 in the data set?

makvit [3.9K]

D is the answer for this question:))

8 0

3 years ago

A school typically sells 500 yearbooks in a year for $50 dollars each.

Evgen [1.6K]

You divide 500 by $50 to get 10; the school sold 10 yearbooks that year if you’re looking for that as an answer.

8 0

3 years ago

Read 2 more answers

PLEASE HELP!!!! i REALLY NEED TO GET THIS DONE AND AM HAVING TROUBLE WITH THIS ONE!!!!

zubka84 [21]

Answer:

a[n] = a[n-1]×(4/3)

a[1] = 1/2

Step-by-step explanation:

The terms of a geometric sequence have an initial term and a common ratio. The common ratio multiplies the previous term to get the next one. That sentence describes the recursive relation.

The general explicit term of a geometric sequence is ...

a[n] = a[1]×r^(n-1) . . . . . where a[1] is the first term and r is the common ratio

Comparing this to the expression you are given, you see that ...

a[1] = 1/2

r = 4/3

(You also see that parenthses are missing around the exponent expression, n-1.)

A recursive rule is defined by two things:

the starting value(s) for the recursive relation
the recursive relation relating the next term to previous terms

The definition of a geometric sequence tells you the recursive relation is:

<em>the next term is the previous one multiplied by the common ratio</em>.

In math terms, this looks like

a[n] = a[n-1]×r

Using the value of r from above, this becomes ...

a[n] = a[n-1]×(4/3)

Of course, the starting values are the same for the explicit rule and the recursive rule:

a[1] = 1/2

7 0

3 years ago