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3 years ago

A number cube is rolled. What is the probability that it will land on a 2 or a 5?

2 answers:

7 0

A cube has 6 sides. 2 and 5 are numbers on 2 of the cube's sides. The probability is therefore 2/6 which simplifies to 1/3 or ~33.3%

zimovet [89]3 years ago

3 0

It’s morn of its 292 thanks.

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Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 w

irina1246 [14]

Answer:

A 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus is [0.012, 0.270].

Step-by-step explanation:

We are given that Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 24 students, she finds 2 who eat cauliflower.

Firstly, the pivotal quantity for finding the confidence interval for the population proportion is given by;

P.Q. = $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ~ N(0,1)

where, $\hat p$ = sample proportion of students who eat cauliflower

n = sample of students

p = population proportion of students who eat cauliflower

Here for constructing a 95% confidence interval we have used a One-sample z-test for proportions.

So, 95% confidence interval for the population proportion, p is ;

P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5% level

of significance are -1.96 & 1.96}

P(-1.96 < $\frac{\hat p-p}{\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < 1.96) = 0.95

P( $-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < ${\hat p-p}$ < $1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

P( $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ < p < $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ) = 0.95

Now, in Agresti and Coull's method; the sample size and the sample proportion is calculated as;

$n = n + Z^{2}__(\frac{_\alpha}{2})$

n = $24 + 1.96^{2}$ = 27.842

$\hat p = \frac{x+\frac{Z^{2}__(\frac{\alpha}{2}_) }{2} }{n}$ = $\hat p = \frac{2+\frac{1.96^{2} }{2} }{27.842}$ = 0.141

95% confidence interval for p = [ $\hat p-1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ , $\hat p+1.96 \times {\sqrt{\frac{\hat p(1-\hat p)}{n} } }$ ]

= [ $0.141 -1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ , $0.141 +1.96 \times {\sqrt{\frac{0.141(1-0.141)}{27.842} } }$ ]

= [0.012, 0.270]

Therefore, a 95% confidence interval for the proportion of students who eat cauliflower on Jane's campus [0.012, 0.270].

The interpretation of the above confidence interval is that we are 95% confident that the proportion of students who eat cauliflower on Jane's campus is between 0.012 and 0.270.

7 0

3 years ago

How many periods of time, each 1/6 of an hour long, does a 10-hour period of time represent?

Allisa [31]

Answer:

60 mintues

Step-by-step explanation:

1/6 of 60= 6

10 hours= 600 minutes

600÷6= 60 mintues

5 0

3 years ago

Read 2 more answers

Name 2 or 3 you know about variable and how

ololo11 [35]

Answer:

a variable is an unknown number, the point of algebra is to solve for the. they are represented by letters, 5x is an example.

Step-by-step explanation: skillz

7 0

3 years ago

What is the product in scientific notation?

sashaice [31]

(2.5 × $10^{-10}$ ) × (7 × $10^{-6}$ )

First, simplify brackets. / Your problem should look like: 2.5 × $10^{-10}$ × 7 × $10^{-6}$
Second, simplify. / Your problem should look like: 17.5 × $10^{-10}$ × $10^{-6}$
Third, simplify exponent. / Your problem should look like: 17.5 × $10^{-15}$

Answer: B

3 0

3 years ago

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Solve the following equation. then place the correct number in the box provided. 2x + 1 < 9

allsm [11]

I think the answer is 4

8 0

3 years ago