Similar triangles ... help?

Assume that the empirical rule is a good model for the time it takes for all passengers to board an airplane. The mean time is 4

slamgirl [31]

Answer:

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

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:

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

The Z-score measures how many standard deviations the measure is from the mean. 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, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

$\mu = 48, \sigma = 4$ .

Which interval describes how long it takes for passengers to board the middle 95% of the time?

This is between the 2.5th percentile and the 97.5th percentile.

So this interval is the value of X when Z has a a pvalue of 0.025 and the value of X when Z has a pvalue of 0.975

Lower Limit

Z has a pvalue of 0.025 when $Z = -1.96$ . So

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

$-1.96 = \frac{X - 48}{4}$

$X - 48 = -1.96*4$

$X = 40.16$

Upper Limit

Z has a pvalue of 0.975 when $Z = 1.96$ . So

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

$1.96 = \frac{X - 48}{4}$

$X - 48 = 1.96*4$

$X = 55.84$

The interval that describes how long it takes for passengers to board the middle 95% of the time is between 40.16 minutes and 55.84 minutes.

7 0

3 years ago

Find an expression for the perimeter of rectangle ABCD. Use the formula P= 2l + 2w.

natita [175]

Answer:

(b)

P = [4(4a + 3b]/(2a + b)

Step-by-step explanation:

P = 2L + 2W

P = [2(5a + 4b) + 2(3a + 2b)]/(2a + b)

P = [10a + 8b + 6a + 4b]/(2a + b)

P = [16a + 12b]/(2a + b)

P = [4(4a + 3b]/(2a + b)

3 0

3 years ago

PLEASE HELP WITH THESE QUESTIONS! WILL GIVE 100 POINTS!

Oduvanchick [21]

Answer:

1. 1/6 2. 80

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers

What are two decimals that are equivalent to 7.7

Elza [17]

7.70 and 7.700 they are all the same since the 7 tenths are still in its place

8 0

3 years ago

Terry and Callie do word processing. For a certain prospectus Callie can prepare it two hours faster than Terry can. If they wor

Dahasolnce [82]

Time taken by jerry alone is 10.1 hours

Time taken by callie alone is 8.1 hours

Solution:

Given:- For a certain prospectus Callie can prepare it two hours faster than Terry can

Let the time taken by Terry be "a" hours

So, the time taken by Callie will be (a-2) hours

Hence, the efficiency of Callie and Terry per hour is $\frac{1}{a-2} \text { and } \frac{1}{a} \text { respectively }$

If they work together they can do the entire prospectus in five hours

$\text {So, } \frac{1}{a-2}+\frac{1}{a}=\frac{1}{5}$

On cross-multiplication we get,

$\frac{a+(a-2)}{(a-2) \times a}=\frac{1}{5}$

$\frac{2 a-2}{(a-2) \times a}=\frac{1}{5}$

On cross multiplication ,we get

$\begin{array}{l}{5 \times(2 a-2)=a \times(a-2)} \\\\ {10 a-10=a^{2}-2 a} \\\\ {a^{2}-2 a-10 a+10=0} \\\\ {a^{2}-12 a+10=0}\end{array}$

using quadratic formula:-

$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

$x=\frac{12 \pm \sqrt{144-40}}{2}$

$\begin{array}{l}{x=\frac{12 \pm \sqrt{144-40}}{2}} \\\\ {x=\frac{12 \pm \sqrt{104}}{2}} \\\\ {x=\frac{12 \pm 2 \sqrt{26}}{2}} \\\\ {x=6 \pm \sqrt{26}=6 \pm 5.1} \\\\ {x=10.1 \text { or } x=0.9}\end{array}$

If we take a = 0.9, then while calculating time taken by callie = a - 2 we will end up in negative value

Let us take a = 10.1

So time taken by jerry alone = a = 10.1 hours

Time taken by callie alone = a - 2 = 10.1 - 2 = 8.1 hours

3 0

3 years ago