X:2 (105-275:11):4=28

Mark rolls 2 fair dice and adds the results from each.

Natali5045456 [20]

Answer:

P ( X > 5 ) = 72,2 %

Step-by-step explanation:

The probability of success ( outcomes bigger than 5 )

If dice 1 outcome is 6 no matter wich outcome we get from dice 2 all events are successful, the we have 6 outcomes

If dice 1 outcome is 5 we also have 6 outcomes

If dice 1 outcomes is 4 we have 5 positive outcomes

If dice 1 outcome is 3 we have 4 positive outcomes

If dice 1 outcome is 2 we have 3 positive outcomes

if dice 1 outcome is 1 we have 2 positive outcomes

Total evaluating dice 1: positive outcomes 26

We will get the sames results analysing dice 2 then we have a total of

52 successful events

And total numbers of outcomes is 36 + 36 = 72

Then

P ( X > 5 ) = 52/72

P ( X > 5 ) = 0,722

P ( X > 5 ) = 72,2 %

7 0

3 years ago

Suppose you are working in an insurance company as a statistician. Your manager asked you to check police records of car acciden

pochemuha

Answer:

(a) 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We conclude that the the percentage of teenagers has not changed since you join the company.

(d) We conclude that the the percentage of teenagers has changed since you join the company.

Step-by-step explanation:

We are given that your manager asked you to check police records of car accidents and out of 576 accidents you selected randomly, teenagers were at the wheel in 120 of them.

(a) Firstly, the pivotal quantity for 95% 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 teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

p = population percentage of all car accidents

Here for constructing 95% confidence interval we have used One-sample z proportion statistics.

So, 95% confidence interval for the population population, 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

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

= [ $0.21-1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ , $0.21+1.96 \times {\sqrt{\frac{0.21(1-0.21)}{576} }}$ ]

= [0.177 , 0.243]

Therefore, 95% confidence interval for the percentage of all car accidents that involve teenage drivers is [0.177 , 0.243].

(b) We are 95% confident that the percentage of all car accidents that involve teenage drivers will lie between 17.7% and 24.3%.

(c) We are also provided that before you were hired in the company, the percentage of teenagers who where involved in car accidents was 18%.

The manager wants to see if the percentage of teenagers has changed since you join the company.

Let p = percentage of teenagers who where involved in car accidents

So, Null Hypothesis, $H_0$ : p = 18% {means that the percentage of teenagers has not changed since you join the company}

Alternate Hypothesis, $H_A$ : p $\neq$ 18% {means that the percentage of teenagers has changed since you join the company}

The test statistics that will be used here is One-sample z proportion statistics;

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

where, $\hat p$ = sample proportion teenage drivers = $\frac{120}{576}$ = 0.21

n = sample of accidents = 576

So, test statistics = $\frac{0.21-0.18}{\sqrt{\frac{0.21(1-0.21)}{576} }}$

= 1.768

The value of the sample test statistics is 1.768.

Now at 0.05 significance level, the z table gives critical value of -1.96 and 1.96 for two-tailed test. Since our test statistics lies within the range of critical values of z, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the the percentage of teenagers has not changed since you join the company.

(d) Now at 0.1 significance level, the z table gives critical value of -1.6449 and 1.6449 for two-tailed test. Since our test statistics does not lie within the range of critical values of z, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the the percentage of teenagers has changed since you join the company.

4 0

3 years ago

The proportion used to find the average number of trout you would expect to live in the pond is

Ronch [10]

Answer:140

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

Find the x intercept and the y intercept of the graph of the equation 2x+4y=8

maksim [4K]

Answer:

x-intercept: 4

y-intercept: 2

Step-by-step explanation:

finding the x-intercept:

first, substitute y = 0.

2x + 4 x 0 = 8

then, remove the 0.

2x + 0 = 8

then, divide both sides. 2x = 8

so, x = 4.

finding the y-intercept:

first, substitute x = 0.

then, solve.

2 x 0 + 4y = 8

so, y = 2.

3 0

3 years ago

Denisa is saving for a new bicycle. The bicycle cost $89. So far, Denisa has earned $54 babysitting. What percent of the total c

xz_007 [3.2K]

$54/$89 means she has dared 60.6742% or you can round to 60.67%

5 0

2 years ago

Read 2 more answers