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ipn [44]
3 years ago
6

The numerical value of the variance a. is negative if the mean is negative. b. is always larger than the numerical value of the

standard deviation. c. is always smaller than the numerical value of the standard deviation. d. can be larger or smaller than the numerical value of the standard deviation.
Mathematics
1 answer:
Snowcat [4.5K]3 years ago
8 0

Answer:

Step-by-step explanation:

Variance is the sum of squares of all items x from mean.  i.e

Variance = \Sigma (x-xbar)^2

Being the sum of squares variance can never be negative irrespective of mean being negative.

Std deviation is the square root of variances.  This will thus be less than variance if variance >1 other wise std deviation will be bigger than variance.

Hence option d is right.

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The probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7. Assume the tria
zhannawk [14.2K]

Answer:

(a) P(X = 4) = 0.0189

(b) P(X \leq 4) = 0.9919

(c) P(X \geq 4) = 0.027

Step-by-step explanation:

We are given that the probability of a successful optical alignment in the assembly of an optical data storage product is p = 0.7 .

Since we have to find the probabilities for 1st successful alignments, so the probability distribution that we will use here is Geometric distribution.

<u>Geometric distribution</u> is used when we are interested in knowing the chances of our first success.

The probability distribution of geometric distribution is given by;

P(X =x) = p(1-p)^{x-k} ; x = 1,2,3,....

where, x = number of trials

            k = first success = 1

            p = probability of getting success = 0.70

So, X ~ Geo(p = 0.7)

(a) Probability that the 1st successful alignment requires exactly 4 trials is given by = P(X = 4)

Here, x = 4, p = 0.7 and k = 1

So, P(X = 4) = 0.7(1-0.7)^{4-1} = 0.7 \times 0.3^{3} = 0.0189

(b) Probability that the 1st successful alignment requires at most 4 trials is given = P(X \leq 4)

 P(X \leq 4) = P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)  

               = 0.7(1-0.7)^{1-1} + 0.7(1-0.7)^{2-1}+0.7(1-0.7)^{3-1}+0.7(1-0.7)^{4-1}

               = 0.7 \times 0.3^{0}+0.7 \times 0.3^{1}+0.7 \times 0.3^{2}+0.7 \times 0.3^{3}

               = 0.7 + 0.21 + 0.063 + 0.0189 = 0.9919

(c) Probability that the 1st successful alignment requires at least 4 trials is given by = P(X \geq 4)

    P(X \geq 4) = 1 - P(X < 4) = 1 - P(X \leq 3)

    P(X \geq 4) = 1 - P(X = 1) - P(X = 2) - P(X = 3)

                  =  1-0.7(1-0.7)^{1-1} + 0.7(1-0.7)^{2-1}+0.7(1-0.7)^{3-1}

                  = 1-0.7 \times 0.3^{0}+0.7 \times 0.3^{1}+0.7 \times 0.3^{2}

                  = 1 - 0.7 - 0.21 - 0.063 = 0.027

8 0
3 years ago
Solve 5x +3&gt;19 what is it
tatyana61 [14]

Answer:

x > 3 1/5

Step-by-step explanation:

5x +3>19

Subtract 3 from each side

5x +3-3>19-3

5x >16

Divide each side by 5

5x/5 > 16/5

x > 16/5

x > 3 1/5

7 0
3 years ago
Help please
dolphi86 [110]
This is a linear programming question
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while x is n, y is r
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7 0
3 years ago
In ΔEFG, the measure of ∠G=90°, the measure of ∠F=38°, and FG = 6.7 feet. Find the length of EF to the nearest tenth of a foot.
Verizon [17]

Answer:

8.5

Step-by-step explanation:

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3 years ago
Divide 72 in the ratio 7:2
Ksivusya [100]
Do you mean the ratio 1:2
6 0
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