Whats the extreme value?y=3(x+5)^(2)-4

Calculate the sample mean and sample variance for the following frequency distribution of heart rates for a sample of American a

spin [16.1K]

Answer:

$Mean = 68.9$

$s^2 =18.1$ --- Variance

Step-by-step explanation:

Given

$\begin{array}{cccccc}{Class} & {51-58} & {59-66} & {67-74} & {75-82} & {83-90} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

Solving (a): Calculate the mean.

The given data is a grouped data. So, first we calculate the class midpoint (x)

For 51 - 58.

$x = \frac{1}{2}(51+58) = \frac{1}{2}(109) = 54.5$

For 59 - 66

$x = \frac{1}{2}(59+66) = \frac{1}{2}(125) = 62.5$

For 67 - 74

$x = \frac{1}{2}(67+74) = \frac{1}{2}(141) = 70.5$

For 75 - 82

$x = \frac{1}{2}(75+82) = \frac{1}{2}(157) = 78.5$

For 83 - 90

$x = \frac{1}{2}(83+90) = \frac{1}{2}(173) = 86.5$

So, the table becomes:

$\begin{array}{cccccc}{x} & {54.5} & {62.5} & {70.5} & {78.5} & {86.5} \ \\ {Frequency} & {6} & {3} & {11} & {13} & {4} \ \end{array}$

The mean is then calculated as:

$Mean = \frac{\sum fx}{\sum f}$

$Mean = \frac{54.5*4+62.5*3+70.5*11+78.5*13+86.5*4}{6+3+11+13+4}$

$Mean = \frac{2547.5}{37}$

$Mean = 68.9$ -- approximated

Solving (b): The sample variance:

This is calculated as:

$s^2 =\frac{\sum (x - \overline x)^2}{\sum f - 1}$

So, we have:

$s^2 =\frac{(54.5-68.9)^2+(62.5-68.9)^2+(70.5-68.9)^2+(78.5-68.9)^2+(86.5-68.9)^2}{37 - 1}$

$s^2 =\frac{652.8}{36}$

$s^2 =18.1$ -- approximated

5 0

2 years ago

Suppose I claim that the average monthly income of all students at college is at least $2000. Express H0 and H1 using mathematic

pishuonlain [190]

Answer:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): $\mu \geq 2000$

Alternative hypothesis (H1): $\mu$

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 200 or no

Step-by-step explanation:

For this case we want to test if the the average monthly income of all students at college is at least $2000. Since the alternative hypothesis can't have an equal sign thne the correct system of hypothesis for this case are:

Null hypothesis (H0): $\mu \geq 2000$

Alternative hypothesis (H1): $\mu$

And in order to test this hypothesis we can use a one sample t or z test in order to verify if the true mean is at least 2000 or no

7 0

2 years ago

2.85 as a mixed number

WARRIOR [948]

The number 2.85 can be writen using the fraction 285/100 which is equal to 57/20 when reduced to lowest terms.
It is also equal to 2 17/20 when writen as a mixed number.
You can use the following approximate value(s) for this number:57/20 =~ 2 6/7 (if you admit a error of 0.250627%)2.85 =~ 2 5/6 (if you admit a error of -0.584795%)2.85 =~ 3 (if you admit a error of 5.263158%)

3 0

2 years ago

Read 2 more answers

1) Solve for x in the following equation: 7x + 10 - 10x - 5 > 20 *

Olenka [21]

Answer:x<1/7 (5 - sqrt(130))

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

How do I get the answer for #2. What’s the equation to get to the answer please?

Snezhnost [94]

Answer:

GED=2FED. Multiply by 2.

Step-by-step explanation:

The page says that the diagram is not to scale, and that EF bisects(cuts in half equally) GED. Don't go by what it looks like, FED and FEG are equal in size. So each one is 1/2 of GED.

5 0

3 years ago