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Kitty [74]
3 years ago
11

Help fast!! please.

Mathematics
1 answer:
alexira [117]3 years ago
6 0

Answer:

Mean = 10

Variance = 30.89

Standard Deviation = 5.56

Step-by-step explanation:

Find the Mean, Variance and Standard deviation

6, 14, 8, 2, 11, 7, 12, 4, 18, 18

Step 1

We rearrange the data and find the Mean

2, 4, 6, 7, 8, 11, 12, 14, 18, 18

Mean = Sum of values/Number of values

= 2 + 4+ 6+ 7+ 8 + 11 + 12 + 14 + 18 +18/10

= 100/10

= 10

Step 2

We find the variance of this sample days ma

Variance = (x - Mean)²/n - 1

n = 10

Hence,

=( (2 - 10)² +(4 - 10)²+ (6 - 10)²+ (7 - 10)² + (8 - 10)² + (11 - 10)² + (12 - 10)² + (14 - 10)² + (18 - 10)² +(18 - 10)²) /10 -1

= ( 64 + 36 + 16 + 9 + 4 + 1 + 4 + 16 + 64 +64)/9

= 278/9

= 30.88888889

Approximately = 30.89

Step 3

Standard Deviation = √Variance

= √30.89

= 5.5578772926

Approximately = 5.56

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A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose pe
soldier1979 [14.2K]

Using the normal distribution, it is found that:

a) 0.8599 = 85.99% probability that x is more than 60.

b) 0.1788 = 17.88% probability that x is less than 110.

c) 0.6811 = 68.11% probability that x is between 60 and 110.

d) 0.0643 = 6.43% probability that x is greater than 125.

In a normal distribution with mean \mu and standard deviation \sigma, the z-score of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

  • It measures how many standard deviations the measure is from the mean.  
  • After finding the z-score, we look at the z-score table and find the p-value associated with this z-score, which is the percentile of X.

In this problem:

  • The mean is of 87, thus \mu = 87.
  • The standard deviation is of 25, thus \sigma = 25.

Item a:

This probability is <u>1 subtracted by the p-value of Z when X = 60</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{60 - 87}{25}

Z = -1.08

Z = -1.08 has a p-value of 0.1401.

1 - 0.1401 = 0.8599

0.8599 = 85.99% probability that x is more than 60.

Item b:

This probability is the <u>p-value of Z when X = 110</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{110 - 87}{25}

Z = 0.92

Z = 0.92 has a p-value of 0.8212.

1 - 0.8212 = 0.1788.

0.1788 = 17.88% probability that x is less than 110.

Item c:

This probability is the <u>p-value of Z when X = 110 subtracted by the p-value of Z when X = 60</u>.

From the previous two items, 0.8212 - 0.1401 = 0.6811.

0.6811 = 68.11% probability that x is between 60 and 110.

Item d:

This probability is <u>1 subtracted by the p-value of Z when X = 125</u>, thus:

Z = \frac{X - \mu}{\sigma}

Z = \frac{125 - 87}{25}

Z = 1.52

Z = 1.52 has a p-value of 0.9357.

1 - 0.9357 = 0.0643.

0.0643 = 6.43% probability that x is greater than 125.

A similar problem is given at brainly.com/question/24863330

7 0
3 years ago
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