Which of the following tables represents a proportional relationship?

The Statistics Club at Woodvale College sold college Y-shirts as a fundraiser. The result of the sale are shown below. Choose on

zavuch27 [327]

We are asked to find the probability that the student sold 11-15 T-shirts or less than 6 T-shirts.

The total number of club members = 2 + 14 + 12 + 3 + 6 + 1 = 38

Probability of 11-15 T-shirts:

From the table, 3 club members bought 11 - 15 T-shirts.

So the probability is 3/38

Probability of less than 6 T-shirts:

Less than 6 T-shirts means 1 - 5 plus 0 T-shirts.

Form the table, 14 club members bought 1 - 5 T-shirts and 2 club members bought 0 T-shirts.

Total club member who bought 1 - 5 and 0 T-shirts = 14 + 2 = 16

So the probability is 16/38

Now we have to add them together to find the probability that the student sold 11-15 T-shirts or less than 6 T-shirts.

(or means to add)

So the probability is 3/38 + 16/38 = 19/38 = 0.5000

Therefore, the correct answer is option c.

6 0

1 year ago

A sample of 12 radon detectors of a certain type was selected, and each was exposed to 100 pCI/L of radon. The resulting reading

valkas [14]

Answer:

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

$t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921$

$p_v =2*P(t_{11}$

Step-by-step explanation:

1) Data given and notation

Data: 105.6, 90.9, 91.2, 96.9, 96.5, 91.3, 100.1, 105.0, 99.6, 107.7, 103.3, 92.4

We can calculate the sample mean and deviation for this data with the following formulas:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$

$s=\sqrt{\frac{\sum_{i=1}^n (X_i- \bar X)^2}{n-1}}$

The results obtained are:

$\bar X=98.375$ represent the sample mean

$s=0.6.109$ represent the sample standard deviation

$n=12$ sample size

$\mu_o =100$ represent the value that we want to test

$\alpha$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

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

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is equal to 100pCL/L, the system of hypothesis are :

Null hypothesis: $\mu = 100$

Alternative hypothesis: $\mu \neq 100$

Since we don't know the population deviation, is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$t=\frac{98.375-100}{\frac{6.109}{\sqrt{12}}}=-0.921$

4) P-value

First we need to find the degrees of freedom for the statistic given by:

$df=n-1=12-1=11$

Since is a two sided test the p value would given by:

$p_v =2*P(t_{11}$

5) Conclusion

If we compare the p value and the significance level assumed $\alpha=0.05$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can conclude that the true mean is not significant different from 100 at 5% of significance.

3 0

3 years ago

Follow up question how do you do it when it's e^4?

lesya [120]

Ln 54.598... = 4 because ln = log e

5 0

2 years ago

The radius of one sphere is twice as great as the radius of a second sphere. Find the ratio of their volumes.

Juliette [100K]

The ratio of the radii is 2:1, so the ratio of their surface areas is 4:1. The area of a sphere is defined by 4 * pi * r^2 

So if the radius of the first sphere is 2r, then it would be (2r)^2 = 4r^2 

The rest is the same. So the ratio of their surface areas would be 

4 * pi * 4r^2 divided by 
4 * pi * r^2 

or 4.

7 0

3 years ago

No copy and paste answers.

miss Akunina [59]

Answer:

2.5 miles

Step-by-step explanation:

The relation between time, speed, and distance is ...

distance = speed × time

We can define t to be Stanley's swimming time. Then t+0.5 was his running time, and 2(t+0.5) was his biking time. His total distance covered is ...

64 = 9(t +0.5) +16(2(t +0.5)) +2.5(t)

64 = 43.5t +20.5 . . . . . . . simplify

43.5 = 43.5t . . . . . . . . . subtract 20.5

t = 1 . . . . . . . . . . . . . . divide by the coefficient of t

Stanley swam for 1 hour, so the distance he covered while swimming was ...

(2.5 mi/h)(1 h) = 2.5 mi

Stanley covered 2.5 miles while swimming.

_____

Additional comment

Stanley ran for 1.5 hours, covering 9×1.5 = 13.5 miles. He biked for 3 hours, covering 16×3 = 48 miles. His total distance was 2.5 +13.5 +48 = 64 miles, as given.

6 0

2 years ago