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inysia [295]
3 years ago
9

What is the probability of flipping a coin 7 times and getting heads 6 times? Round your answer to the nearest tenth of a percen

t.
A. 16.4%
B. 5.5%
C. 27.3%
D. 0.8%
Mathematics
2 answers:
Thepotemich [5.8K]3 years ago
7 0

Answer:

B. 5.5%

Step-by-step explanation:

For a fair coin,

Probability of a head, P(H) = 1/2 = 0.5

Probability of a tail , P(T) = 1/2 = 0.5

The number of possible outcomes is small enough to simply list the outcome:

The possible outcomes of flipping a coin 7 times and getting heads 6 times are these 7 possibilities:

THHHHHH

HTHHHHH

HHTHHHH

HHHTHHH

HHHHTHH

HHHHHTH

HHHHHHT

The probability of EACH of the above outcomes is

= (0.5)(0.5)(0.5)(0.5)(0.5)(0.5)(0.5)

= (0.5)⁷

Since there are 7 possibilities and since the probabilities of every outcome is identical, the probability of rolling the 7 outcomes is,

= 7 x probability of each outcome

= 7 x (0.5)⁷

= 0.5468

= 5.468%

= 5.5% (nearest tenth)

dedylja [7]3 years ago
3 0
The answer for this would be C.
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5 0
3 years ago
Read 2 more answers
Faced with rising fax costs, a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail inste
Vladimir [108]

Answer:

The value of t test statistics is 5.9028.

We conclude that the true mean is greater than 10 at the .01 level of significance.

Step-by-step explanation:

We are given that a firm issued a guideline that transmissions of 10 pages or more should be sent by 2-day mail instead.

The firm examined 35 randomly chosen fax transmissions during the next year, yielding a sample mean of 14.44 with a standard deviation of 4.45 pages.

<em />

<em>Let </em>\mu<em> = true mean transmission of pages.</em>

So, Null Hypothesis, H_0 : \mu \leq 10 pages     {means that the true mean is smaller than or equal to 10}

Alternate Hypothesis, H_A : \mu > 10 pages     {means that the true mean is greater than 10}

The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;

                        T.S. =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample mean = 14.44 pages

            s = sample standard deviation = 4.45 pages

            n = sample of fax transmissions = 35

So, <u><em>test statistics</em></u>  =  \frac{14.44-10}{\frac{4.45}{\sqrt{35} } }  ~ t_3_4  

                               =  5.9028

(a) The value of t test statistics is 5.9028.

Now, at 0.01 significance level the z table gives critical values of 2.441 at 34 degree of freedom for right-tailed test.

<em>Since our test statistics is more than the critical values of z as 5.9028 > 2.441, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis.</u></em>

Therefore, we conclude that the true mean is greater than 10.

(b) Now, P-value of the test statistics is given by the following formula;

               P-value = P( t_3_4 > 5.9028) = Less than 0.05%    {using t table)

7 0
3 years ago
For her 1st birthday, Ruth's grandparents invested $1000 in an 18-year certificate for her that pays 10% compounded annually. Ho
Lyrx [107]

Answer:

The certificate will be worth $5,559.92 on Ruth's 19th birthday.

Step-by-step explanation:

The compound interest formula is given by:

A = P(1 + \frac{r}{n})^{nt}

Where A is the amount of money, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per unit t and t is the time the money is invested or borrowed for.

In this problem, we have that:

P = 1000, n = 1, r = 0.1, t = 18

So

A = 1000(1 + \frac{0.1}{1})^{1*18}

A = 5559.92

The certificate will be worth $5,559.92 on Ruth's 19th birthday.

7 0
3 years ago
Which pair of triangles can be proven congruent by SAS?
ivolga24 [154]

Answer:

Second option

Step-by-step explanation:

They have two congruent pairs of sides and one congruent pair of angles.

4 0
2 years ago
Find the measure of angle 1
kolbaska11 [484]

Answer:

44°

Step-by-step explanation:

8x - 4 = 6x + 8 (This is because they are corresponding angles)

8x - 6x = 8 + 4

2x = 12

x = 12 ÷ 2

x = 6

6x + 8 = angle 1 (Vertically opposite angles are equal)

Substitute the value of x in the equation '6x +8' to get the size of the angle.

6 × 6 + 8

36 + 8 = 44°

Angle 1  =  44°

3 0
2 years ago
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