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2 years ago

Here is a list of numbers: 8 7 12 7 11 10 7 12

Mathematics

2 answers:

avanturin [10]2 years ago

4 0

Answer:

Ascending order = 7,7,7,8,10,11,12,12

a) n = 8

= median = (n/2+(n/2+1)/2

= (4th term + 5th term)/2

= 8+10/2

= 9

b) range = 12-7 = 5

c) the mode = 7 (highest occuring value)

Natali5045456 [20]2 years ago

3 0

Answer:

the median = 9

the range = 5

the mode = 7

Step-by-step explanation:

7 7 7 8 10 11 12 12

the median = (8+10)/2 = 9

the range = max - min = 12-7 = 5

the mode = 7

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Answer:

The value is $P(X \ge 15) = 0.5$

Step-by-step explanation:

From the question we are told that

The probability of the device failing during the warranty period is $p = 0.005$

The sample size is $n = 3000$

The random variable considered is x = 15

Generally this is distribution is binomial given the fact that there is only two out comes hence

X which is a variable representing a randomly selected selected electronic follows a binomial distribution i.e

$X \~ \ B(n , p)$

Now the mean is mathematically evaluated as

$\mu = n * p$

=> $\mu = 3000 * 0.005$

=> $\mu =15$

The standard deviation is mathematically represented as

$\sigma = \sqrt{np(1 -p )}$

=> $\sigma = \sqrt{3000 * 0.005 * (1 - 0.005 )}$

=> $\sigma = 3.86$

Now given that n is very large, then it mean that we can successfully apply normal approximation on this binomial distribution

$P(X \ge 15) = P( \frac{X - \mu}{\sigma } \ge \frac{x - \mu}{\sigma } )$

Now applying Continuity Correction we have

$P(X \ge (15-0.5)) = P( \frac{X - \mu}{\sigma } > \frac{(15 -0.5) - 15}{3.86 } )$

Generally $\frac{X - \mu}{\sigma } = Z (The \ standardized \ value \ of \ X)$

$P(X \ge (15-0.5)) = P(Z >-0.130 )$

From the z-table

$P(Z >-0.130 ) =0.5$

Thus

$P(X \ge 15) = 0.5$

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