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1 year ago

14

Find probabilities using combinations and permutations. Tyler was feeling particularly adventurous at the hair salon one day, an

d decided to dye his hair. The stylist informed him that he had 10 colors to choose from, 6 of which were shades of purple . If Tyler randomly selects 5 colors and tells the stylist to choose from those, what is the probability that exactly 2 of the chosen hair dyes are shades of purple? Write your answer as a decimal rounded to four decimal places.

1 answer:

Blizzard [7]1 year ago

7 0

There are total of 10 colors to choose.

6 are shades of purple and

4 are not shades of purple.

Tyler selects 5 colors, and exactly 2 are shades of purple. Therefore, the 3 other colors are not shades of purple.

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Claim: The standard deviation of pulse rates of adult males is less than 11 bpm. For a random sample of 132 adult males, the pu

seraphim [82]

Answer:

$\chi^2 =\frac{132-1}{121} 114.49 =123.952$

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=132$ represent the sample size

$\alpha$ represent the confidence level

$s^2 =10.7^2 =114.49$ represent the sample variance obtained

$\sigma^2_0 =11^2=121$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population variance specification is violated, so the system of hypothesis would be:

Null Hypothesis: $\sigma^2 \geq 121$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{132-1}{121} 114.49 =123.952$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 131. And since is a right tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=1-CHISQ.DIST(123.952,131,TRUE)"

5 0

3 years ago

HELP PLEASEEEEEE NO LINKS PLEASE 20PTS!!!!

nevsk [136]

Answer:

$x = 5$

Step-by-step explanation:

$3x + 11 = 26$

$3x = 15$

$x = 5$

5 0

3 years ago

Solve for x.<br> 5x−2(x+1)=14 <br><br> x =

IceJOKER [234]

Answer:

x=16/3

Step-by-step explanation:

5x−2(x+1)=14

Distribute

5x -2x -2 =14

Combine like terms

3x -2 =14

Add 2 to each side

3x-2+2 =14+2

3x=16

Divide each side by 3

3x/3 = 16/3

x=16/3

8 0

3 years ago

Read 2 more answers

If<br> DX/DT= 2cm/s <br> x=-1 <br> y=x^2+1<br> DY/DT=??

kobusy [5.1K]

Answer:

$\frac{dy}{dt}$ = - 4 cm/s

Step-by-step explanation:

Let us revise the chain rule

If $\frac{dy}{dt}$ = a and $\frac{dx}{dt}$ = b, then

$\frac{dy}{dx}$ = $\frac{dy}{dt}$ ÷ $\frac{dx}{dt}$ = $\frac{a}{b}$

∵ y = x² + 1

- Use the differentiation to find $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2x

∵ x = -1

- Substitute x by -1 in $\frac{dy}{dx}$

∴ $\frac{dy}{dx}$ = 2(-1)

∴ $\frac{dy}{dx}$ = -2

∵ $\frac{dy}{dt}$ = $\frac{dy}{dx}$ × $\frac{dx}{dt}$

∵ $\frac{dx}{dt}$ = 2 cm/s

∴ $\frac{dy}{dt}$ = (-2) × (2)

∴ $\frac{dy}{dt}$ = - 4 cm/s

8 0

3 years ago

The loaves of rye bread distributed to a local store by a certain bakery have an average length of 30 centimeters and a standard

cupoosta [38]

Answer:

79.91% of loaves are between 26.94 and 32.18 centimeters

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

$\mu = 30, \sigma = 2$

What percentage of loaves are between 26.94 and 32.18 centimeters

This is the pvalue of Z when X = 32.18 subtracted by the pvalue of Z when X = 26.94.

X = 32.18:

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

$Z = \frac{32.18 - 30}{2}$

$Z = 1.09$

$Z = 1.09$ has a pvalue of 0.8621

X = 26.94:

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

$Z = \frac{26.94 - 30}{2}$

$Z = -1.53$

$Z = -1.53$ has a pvalue of 0.0630

0.8621 - 0.0630 = 0.7991

79.91% of loaves are between 26.94 and 32.18 centimeters

5 0

3 years ago