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4 years ago

9

Adeline sets her music player to randomly select songs from her collection. She has 9 country songs, 11 jazz songs, 3 rap songs,

and 6 pop songs. What is the probability that the next song is a rap song or a pop song?
A. 9/29
B. 12/29
C. 14/29
D. 15/29

1 answer:

solong [7]4 years ago

6 0

Answer:

A

Step-by-step explanation:

(3+6)/(9+11+3+6)

= 9/29

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The Ohio Department of Agriculture tested 203 fuel samples across the state

Rus_ich [418]

Answer:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

Step-by-step explanation:

Previous concept

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The population proportion have the following distribution

$p \sim N(p,\sqrt{\frac{p(1-p)}{n}})$

Solution to the problem

In order to find the critical value we need to take in count that we are finding the interval for a proportion, so on this case we need to use the z distribution. Since our interval is at 99% of confidence, our significance level would be given by $\alpha=1-0.99=0.01$ and $\alpha/2 =0.005$ . And the critical value would be given by:

$z_{\alpha/2}=-2.58, z_{1-\alpha/2}=2.58$

The proportion estimated would be:

$\hat p = \frac{14}{105}= 0.133$

And that represent the proportion of failures.

The confidence interval for the mean is given by the following formula:

$\hat p \pm z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}$

If we replace the values obtained we got:

$0.133 - 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.0475$

$0.133 + 2.58\sqrt{\frac{0.133(1-0.133)}{105}}=0.2185$

The 99% confidence interval would be given by (0.0475;0.2185)

3 0

3 years ago

Read 2 more answers

Given the set of data below, which measure(s) will change if the outlier is removed? (Check all that

9966 [12]

Answer:

The mean will change. The range will change.

Step-by-step explanation:

The outlier is 4, it's the one number in the data that isn't close to the other numbers.

The data without the outlier will be 7, 9, 9, 10.

Mode: The mode will still be 9. It is still the number that appears the most in the data.

Median: The median WON'T change. The data is now one value shorter, but the median will still be 9. Before it was 9, and now it's still 9 ((9+9)/2).

Mean: The mean will change because we're excluding one value. Before, the mean was 7.8 (4+7+9+9+10=39, 39/5 = 7.8). NOW it is 8.75 (7+9+9+10=35, 35 / 4 = 8.75).

Range: The range will change. Before it was 10-4, now it is 10-7. The range was originally 6 and now it's 3.

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What is the volume of a cylinder that has the following measurements? area of each base: 50.24 ft2 area of lateral surface: 75.3

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Answer:

150.72 ft³

Step-by-step explanation:

<u>Given:</u>

Area of the base :

B = 50.24 ft²

Height of cylinder:

h = 3 ft

<u>The volume is:</u>

V = Bh
V = 50.24*3 = 150.72 ft³

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3 years ago

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Find the annual interest rate.<br> I = $40, P = $500, t = 16 months

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3 years ago

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Answer:

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