The normal distribution, also known as the bell curve, is a distribution that occurs naturally in many situations of life. We use the model $N(\mu,\sigma)$ to understand the behavior of some real-life variables. Where $\mu$ is the mean value and $\sigma$ is the standard deviation.

In our case, we have

$\mu=1143,\ \sigma=88$

And are required to find the percentage of steers whose weigh lie within a given range. We must use some sort of table or digital means to compute the values because the normal distribution cannot be calculated directly by a formula. We use the NORMDIST (or NORM.DIST) formula for Excel which gives us the left tail of the area behind the bell curve, i.e. the cumulative percentage for a give value of X. The formula has the form

NORM.DIST(x,mean,standard_dev,cumulative)

a) X<1200

The formula is used with the following parameters

NORM.DIST(1200,1143,88,true)

and we get

$P(X$

b) We need to compute P(1100<X<1250). To do this, we calculate both left tails and the subtract them

NORM.DIST(1100,1143,88,true)=0.3125

NORM.DIST(1250,1143,88,true)=0.8880

$P(1100$

$\boxed{P(1100$

6 0

3 years ago

A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 34

VikaD [51]

Answer:

41.6 centimeters

Step-by-step explanation:

The right triangle formula: c^2 = a^2 + b^2

c is the hypotenuse side of the triangle

a and b are the legs of the triangle.

Find the hypotenuse : c^2 = (24)^2 + (34)^2

c = square root of ( (24)^2 + (34)^2)

c = square root of ( 576 + 1,156)

c = 41.6173

5 0

3 years ago