The blood platelet counts of a group of women have a bell-shaped distribution with a mean of and a standard deviation of . (All units are 1000 cells/L.) Using the empirical rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within standard of the mean, or between and ?
b. What is the approximate percentage of women with platelet counts between and ?

Answers

Answer 1

Answer:

Answer:

(a) Approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) Approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Step-by-step explanation:

The complete question is: The blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1. (All units are 1000 cells/mul.) using the empirical rule, find each approximate percentage below.

a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7?

b. What is the approximate percentage of women with platelet counts between 65.2 and 431.8?

We are given that the blood platelet counts of a group of women have a bell-shaped distribution with a mean of 248.5 and a standard deviation of 61.1.

Let X = the blood platelet counts of a group of women

The z-score probability distribution for the normal distribution is given by;

Z = $(X-\mu)/(\sigma)$ ~ N(0,1)

where, $\mu$ = population mean = 248.5

$\sigma$ = standard deviation = 61.1

Now, the empirical rule states that;

68% of the data values lie within 1 standard deviation away from the mean.

95% of the data values lie within 2 standard deviations away from the mean.

99.7% of the data values lie within 3 standard deviations away from the mean.

(a) The approximate percentage of women with platelet counts within 2 standard deviations of the mean, or between 126.3 and 370.7 is given by;

As we know that;

P( $\mu-2\sigma$ < X < $\mu+2\sigma$ ) = 0.95

P(248.5 - 2(61.1) < X < 248.5 + 2(61.1)) = 0.95

P(126.3 < X < 370.7) = 0.95

Hence, approximately 95% of women with platelet counts within 2 standard deviations of the mean.

(b) The approximate percentage of women with platelet counts between 65.2 and 431.8 is given by;

Firstly, we will calculate the z-scores for both the counts;

z-score for 65.2 = $(X-\mu)/(\sigma)$

= $(65.2-248.5)/(61.1)$ = -3

z-score for 431.8 = $(X-\mu)/(\sigma)$

= $(431.8-248.5)/(61.1)$ = 3

This means that approximately 99.7% of women have platelet counts between 65.2 and 431.8.

Answer 2

Answer:

Final answer:

Using the empirical rule, approximately 68% of values fall within 1 standard deviation from the mean in a bell-shaped distribution. For ranges 2 or 3 standard deviations from the mean, the respective approximate percentages are 95% and 99.7%.

Explanation:

The question refers to the Empirical rule, which in statistics, is also known as the Three-sigma rule or the 68-95-99.7 rule. This rule is a shortcut for remembering the proportion of values in a normal distribution that are within a given distance from the mean: 68% are within 1 standard deviation, 95% are within 2 standard deviations, and 99.7% are within 3 standard deviations.

Without given specific values for the mean or standard deviations, we can discuss the problem in a general sense:

For part a, the percentage of women with platelet counts within 1 standard deviation from the mean is approximately 68% under the Empirical rule.
For part b, it depends on how many standard deviations from the mean the range mentioned lies. If it refers to two standard deviations from the mean, then 95% of women would fall into this range, if it refers to three standard deviations, then approximately 99.7% would be the case.

Learn more about Empirical Rule here:

brainly.com/question/35669892

#SPJ3

Related Questions

g let X be a normally distributed random variable with mean 3 and variance 4. a) Let Y = 5X+2. What is the distribution of Y? What are its mean and variance? b) Find P(Y<10). Find P(X<10). c) What is the 99th percentile of the distribution of Y? d) What is the 99th percentile of the distribution of X? e) What is the distribution of W = exp(Y)? What are its mean and variance?
Kristl has saved 30%of her tuition fordance class. Sheneeds to have $600save. How much hasshe saved so far?
Does anyone know the answer
What is the area of this triangle? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth. in² The figure contains a triangle. One side is 11.1 inches. A second side is 7 inches. The angle between the given sides is 84 degrees.
Given the formula below, solve for x. y - y1 = m(x-x1)

Question: What is 32^2?

Answers

Answer: The answer is 1,024.

Explanation: 32^2 is 32 x 32, which is 1,024.

1,024

Explanation: calculator

How do i solve this question.

Answers

try a protractor to solve it

The some of three consecutive integer is 48. find the numbers

Answers

The awser is 13 + 14+ 15

Celia bought a bag of 121212 goldfish for \$3$3dollar sign, 3.What is the cost of 111 goldfish?

Answers

Answer: $0.25

Step-by-step explanation:

We are given that the cost of 12 goldfish = $3

To find the cost of one goldfish we use division operator and divide the cost of 12 gold fishes by 12.

Then , the cost of one gold fish = $\$3/ 12$

⇒ Cost of 1 gold fish $=(\$3)/(12)$

⇒ Cost of 1 gold fish $=(\$1)/(4)$ [Divide numerator and denominator by 3.]

⇒ Cost of 1 gold fish $=\$0.25$ [Simplify by dividing 1 by 4]

Therefore , the cost of 1 goldfish = $0.25

Answer:

0.25

Step-by-step explanation:

I DONT WANT HOW TO DO IT JUST THE ANSWER

Answers

56 trust me homie yuh

Answer:

87.5

Edited: Yea should be 56, misread it LOL.

Appoligise to that silly mistake

Step-by-step explanation:

The following is known about three numbers: If the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2. The third number plus 3 times the first number is -1. The first number plus 3 times the second number plus the third number is -16. Find the sum of the three numbers.

Answers

Answer:

-6

Step-by-step explanation:

Let the first, second and third number be x, y and z respectively.

We are told that the second number is subtracted from the sum of the first number and 3 times the third number, the result is 2.

Thus;

(x + 3z) - y = 2 - - - (eq 1)

The third number plus 3 times the first number is -1.

Thus;

z + 3x = -1 - - - (eq 2)

The first number plus 3 times the second number plus the third number is -16.

Thus;

x + 3y + z = -16 - - - (eq 3)

From eq 2, we can rearrange to get;

z = -1 - 3x

Putting -1 - 3x for z in eq(1) and (eq 3),we have;

(x + 3(-1 - 3x)) - y = 2

x -3 - 9x - y = 2

-8x - y = 2 + 3

-8x - y = 5

y = -5 - 8x

Putting y = -5 - 8x and z = -1 - 3x into eq(3), we have;

x + 3(-5 - 8x) + (-1 - 3x) = -16

x - 15 - 24x - 1 - 3x = -16

-26x - 16 = -16

-26x = 16 + 16

x = 0

Since y = -5 - 8x, then y = -5 - 8(0)

y = - 5

Also, since z = -1 - 3x, then;

z = -1 - 3(0)

z = -1

The sum of the three numbers are;

x + y + z = 0 + (-5) + (-1) = -6

Other Questions

Which shows the expression below simplified?0.42 + (3.5 × 10-2)

The following rule describes the relationship between x and y.Rule: Multiply x by 4 to get y.Complete the table for the given rule.X Y0 __1 __2 __

Find the measure of 0. (to the nearest tenth).A) 36.9B) 38.7C) 51.3D) 53.1

Carpetland salespersons average $8000 per week in sales. Steve Contois, the firm's vice president, proposes a compensation plan with new selling incentives. Steve hopes that the results of a trial selling period will enable him to conclude that the compensation plan increases the average sales per salesperson. a. Develop the appropriate null and alternative hypotheses.