19.2 is what percent of 24

A normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97. What percentage of values lies between

lana [24]

Answer:

63% of the values lies between 70 and 85.

Step-by-step explanation:

We are given that a normally distributed set of numbers has a mean of 75 and a standard deviation of 7.97.

Let X = Set of numbers

The z-score probability distribution for is given by;

Z = $\frac{ X -\mu}{\sigma}$ ~ N(0,1)

where, $\mu$ = mean value = 75

$\sigma$ = standard deviation = 7.97

The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.

So, percentage of values that lies between 70 and 85 is given by = P(70 < X < 85) = P(X < 85) - P(X $\leq$ 70)

P(X < 85) = P( $\frac{ X -\mu}{\sigma}$ < $\frac{ 85-75}{7.97}$ ) = P(Z < 1.25) = 0.89435 {using z table}

P(X $\leq$ 70) = P( $\frac{ X -\mu}{\sigma}$ $\leq$ $\frac{ 70-75}{7.97}$ ) = P(Z $\leq$ -0.63) = 1 - P(Z < 0.63)

= 1 - 0.73565 = 0.26435

Now, in the z table the P(Z $\leq$ x) or P(Z < x) is given. So, the above probability is calculated by looking at the value of x = 1.25 and x = 0.63 in the z table which has an area of 0.89435 and 0.73565 respectively.

Therefore, P(70 < X < 85) = 0.89435 - 0.26435 = 0.63 or 63%

Hence, 63% of the values lies between 70 and 85.

6 0

3 years ago

PLEASE HELP

zmey [24]

Law of cosines :

The law of cosines establishes:

$c ^ 2 = a ^ 2 + b ^ 2 - 2*a*b*cosC.$

general guidelines:

The law of cosines is used to find the missing parts of an oblique triangle (not rectangle) when either the two-sided measurements and the included angle measure are known (SAS) or the lengths of the three sides (SSS) are known.

Law of the sines:

In ΔABC is an oblique triangle with sides a, b, and c, then:

$\frac{a}{sinA} =\frac{b}{sinB} =\frac{c}{sinC}$

The law of the sines is the relation between the sides and angles of triangles not rectangles (obliques). It simply states that the ratio of the length of one side of a triangle to the sine of the angle opposite to that side is equal for all sides and angles in a given triangle.

General guidelines:

To use the law of the sines you need to know either two angles and one side of the triangle (AAS or ASA) or two sides and an opposite angle of one of them (SSA).

The ambiguous case :

If two sides and an angle opposite one of them is given, three possibilities may occur.

(1) The triangle does not exist.

(2) Two different triangles exist.

(3) Exactly a triangle exists.

If we are given two sides and an included angle of a triangle or if we are given 3 sides of a triangle, we can not use the law of the sines because we can not establish any proportion where sufficient information is known. In these two cases we must use the law of cosines

3 0

3 years ago

Grade 8- The Pythagorean Theorem

aleksandr82 [10.1K]

1) pythagorean theorem = a2 + b2 = c2
SO:
10^2 + 6^2 = c2
100 + 36 = c2
136 = c2
Diagonal should equal about 11.66 meters

2) pythagorean theorem = a2 + b2 = c2
SO:12.7^2 + 8.9^2 = c2
161.29 + 79.21 = c2
240.5 = c2
Elevation should equal about 15.1 degrees

8 0

3 years ago

Select all of the situations that represent a linear relationship between x and y.

Harrizon [31]

Answer:

Linear relationship always produces a straight line and are without exponential.

Lets check all the given options:

1. the total area, in square meters, y, of a square garden if the side length is x meters.

The area of a square is

Here, side is 'x' and area 'y' will be .

This is not linear.

2. the height, y, of a 6-foot tree that grows 0.2 feet per month for x months

The equation forms:

When x = 1

When x = 2

=>

When x = 3

=>

This is a linear relation.

3. the total cost, y, of a ski rental from a company that charges $15 plus an additional $8 per day rented for x days

The equation forms:

When x = 1

When x = 2

=>

When x = 3

=>

This is also linear.

4. the total miles, y, traveled by a car going 62 miles per hour in x hours

The equation forms:

When x = 1

When x = 2

=>

When y = 3

=>

This is also linear in nature.

Read more on Brainly.com - brainly.com/question/12747906#readmore

6 0

4 years ago

Read 2 more answers

Determine whether the underlined value is a parameter or a statistic. One of the greatest baseball hitters of all time has a car

Ad libitum [116K]

Answer:

B. The value is a parameter because the career at-bats of a baseball player are a population.

Step-by-step explanation:

The hitter had a career batting average of 0.366.

This value comes from information about the population of every time he has ever gone up to bat. Therefore, it is a parameter.

If on the other hand, we take the batting average of 5 games, the 5 games will be a sample and the batting average will be a statistic.

5 0

4 years ago