Best answer gets Brainliest!!!

Exhibit 6-5 The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation o

hjlf

Answer:

46.18% of the items will weigh between 6.4 and 8.9 ounces.

Step-by-step explanation:

We are given that the weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

Let X = weight of items produced by a machine

The z-score probability distribution for is given by;

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

where, $\mu$ = mean weight = 8 ounces

$\sigma$ = standard deviation = 2 ounces

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 items that will weigh between 6.4 and 8.9 ounces is given by = P(6.4 < X < 8.9) = P(X < 8.9 ounces) - P(X $\leq$ 6.4 ounces)

P(X < 8.9) = P( $\frac{ X -\mu}{\sigma}$ < $\frac{ 8.9-8}{2}$ ) = P(Z < 0.45) = 0.67364 {using z table}

P(X $\leq$ 70) = P( $\frac{ X -\mu}{\sigma}$ $\leq$ $\frac{ 6.4-8}{2}$ ) = P(Z $\leq$ -0.80) = 1 - P(Z < 0.80)

= 1 - 0.78814 = 0.21186

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 = 0.45 and x = 0.80 in the z table which has an area of 0.67364 and 0.78814 respectively.

Therefore, P(6.4 < X < 8.9) = 0.67364 - 0.21186 = 0.4618 or 46.18%

Hence, 46.18% of the items will weigh between 6.4 and 8.9 ounces.

8 0

4 years ago

Convert 28.7251° to degrees, minutes, and seconds. Round to the nearest second.

Leni [432]

28.7251 =

28 degrees

then take the decimal and multiply by 60 to get the minutes

so 0.7251 *60 = 43.506, use the whole number (43)

so now you have 28 degrees, 43 minutes

now take the remaining decimal ( 0.506) and multiply by 60

0.506*60= 30.36

when you have a decimal left over for the seconds, keep that as is.

so you now have 28 degrees, 43 minutes and 30.36 seconds

use ' for minutes and " for seconds

28 degrees 43' 30.36"

8 0

3 years ago

What is the sedition of ratio

Charra [1.4K]

The ratio of sediment yield of a drainage basin to the total amount of sediment moved by sheet erosion and channel erosion.

4 0

3 years ago

Which of the following sums would be under the radical symbol to find the distance between the points (7, -1) and (-8, -9)?

fomenos

The "distance formula" an extension of the Pythagorean Theorem is:

d^2=(x2-x1)^2+(y2-y1)^2 in this case:

d^2=(-8-7)^2+(-9--1)^2

d^2=(-15)^2+(-8)^2

d^2=15^2+8^2

d=√(15^2+8^2)

So the answer is 15^2+8^2

5 0

4 years ago

Triangle inequality theorem-are the lengths 7, 4, and 2 of a triangle possible?

kakasveta [241]

You can't make a triangle with those lengths for sides.

The way I look at it is like this:

-- Take 2 sticks ... lengths 4 and 2 ... and connect them together at one end.

-- The farthest they can reach, if they're opened up completely and pointing
in opposite directions, is a distance of 6 .

-- They can't reach the ends of a stick that is 7 long. So you can't make
a triangle with those 3 sticks.

6 0

4 years ago