Megan and her sister are planning their

A particular Spotify playlist contains 105 songs, of which 10 are by the Beatles. Suppose the shuffle feature is used to play th

katovenus [111]

Answer: The required probability is 0.3296.

Step-by-step explanation:

Since we have given that

Number of songs = 105

Number of songs are by the Beatles = 10

So, Number of songs are not by the Beatles = 105-10=95

So, the probability that the first Beatles song heard is the fifth song played is given by

$\dfrac{^{95}C_4\times ^{10}C_1}{^{105}C_5}\\\\=0.3296$

Hence, the required probability is 0.3296.

8 0

3 years ago

in a program designed to help patients stop smoking 232 patients were given sustained care and 84.9% of them were no longer smok

grandymaker [24]

Answer:

$z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869$

$p_v =2*P(Z>1.869)=0.0616$

If we compare the p value obtained and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .

Step-by-step explanation:

1) Data given and notation

n=232 represent the random sample taken

X represent the adults were no longer smoking after one month

$\hat p=0.849$ estimated proportion of adults were no longer smoking after one month

$p_o=0.80$ is the value that we want to test

$\alpha=0.05$ represent the significance level

Confidence=95% or 0.95

z would represent the statistic (variable of interest)

$p_v$ represent the p value (variable of interest)

2) Concepts and formulas to use

We need to conduct a hypothesis in order to test the claim that the true proportion is 0.8.:

Null hypothesis: $p=0.8$

Alternative hypothesis: $p \neq 0.8$

When we conduct a proportion test we need to use the z statistic, and the is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

The One-Sample Proportion Test is used to assess whether a population proportion $\hat p$ is significantly different from a hypothesized value $p_o$ .

3) Calculate the statistic

Since we have all the info requires we can replace in formula (1) like this:

$z=\frac{0.849 -0.8}{\sqrt{\frac{0.8(1-0.8)}{232}}}=1.869$

4) Statistical decision

It's important to refresh the p value method or p value approach . "This method is about determining "likely" or "unlikely" by determining the probability assuming the null hypothesis were true of observing a more extreme test statistic in the direction of the alternative hypothesis than the one observed". Or in other words is just a method to have an statistical decision to fail to reject or reject the null hypothesis.

The significance level provided $\alpha=0.05$ . The next step would be calculate the p value for this test.

Since is a bilateral test the p value would be:

$p_v =2*P(Z>1.869)=0.0616$

If we compare the p value obtained and the significance level given $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and we can said that at 5% of significance the proportion of adults were no longer smoking after one month is not significantly different from 0.8 or 80% .

6 0

3 years ago

I need the lines slope

Vedmedyk [2.9K]

Step-by-step explanation:

For every 3 squares across, the line goea down 1 square.

Hence the slope is -1/3.

8 0

3 years ago

IM IN A TEST NOW WILL AWARD BRAINLIEST!!!!!

Oksanka [162]

The product has decreased by 80 %

Solution:

The product of the original numbers: xy

One number is decreased by 75 %

Let x be the number decreased by 75 %

new number = x - 75 % of x

$new\ number = x - 75 \% \times x\\\\new\ number = x(1-75 \%)\\\\new\ number = x(1-\frac{75}{100}) = x(1-0.75) = 0.25x$

Another number is decreased by 20 %

Let y be the number decreased by 20 %

new number = y - 20 % of y

$new\ number = y - 20 \% y\\\\new\ number = y(1-20 \%)\\\\new\ number = y(1-\frac{20}{100}) = y(1-0.2) = 0.8y$

Now the product is given as:

$product = 0.25x \times 0.8y = 0.2xy$

Now we have to find the percent decreased

Subtract new product and original product and then divide by original product . Multiply the result by 100 to get percentage

$percent\ decrease = \frac{0.2xy - xy}{xy} \times 100\\\\percent\ decrease = \frac{-0.8xy}{xy} \times 100 = -0.8 \times 100 = -80$

Here negative sign denotes decrease

Thus the product has decreased by 80 %

3 0

3 years ago

Brand Number of Packets Cost

Sveta_85 [38]

Answer:

B) Brand 2

Step-by-step explanation:

Brand 1: $10.68 ÷ 12 = 0.89

Brand 2: $9.44 ÷ 16 = 0.59

Brand 3: $15.30 ÷ 18 = 0.85

Brand 4: $21.84 ÷ 24 = 0.91

Brand 5: $20.40 ÷ 30 = 0.68

Least cost per packet is of Brand 2

3 0

3 years ago

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