Mathematics, 03.10.2019 00:30 ErrorNameTaken505

Correct answer only !

use technology or a z-score table to answer the question.

the lengths of green beans for sale at a supermarket are normally distributed with a mean of 11.2 centimeters and a standard deviation of 2.1 centimeters. consider a bag of 150 green beans.

how many green beans will be 13 centimeters or shorter?

Correct answer only ! use technology or a z-score table to answer the question.

Answers: 2

Show answers

Answers

Answer from: jona187

Choice C: approximately 121 green beans will be 13 centimeters or shorter.

Step-by-step explanation:

What's the probability that a green bean from this sale is shorter than 13 centimeters?

Let the length of a green bean be centimeters.

follows a normal distribution with

mean $\mu = 11.2$ and standard deviation $\sigma = 2.1$ .

In other words,

$X\sim \text{N}(11.2, 2.1^{2})$ ,

and the probability in question is $X \le 13$ .

Z-score table approach:

Find the z-score of this measurement:

$\displaystyle z= \frac{x-\mu}{\sigma} = \frac{13-11.2}{2.1} = 0.857143$ . Closest to 0.86.

Look up the z-score in a table. Keep in mind that entries on a typical z-score table gives the probability of the left tail, which is the chance that will be less than or equal to the z-score in question. (In case the question is asking for the probability that is greater than the z-score, subtract the value from table from 1.)

$P(X\le 13) = P(Z \le 0.857143) \approx 0.8051$ .

"Technology" Approach

Depending on the manufacturer, the steps generally include:

Locate the cumulative probability function (cdf) for normal distributions.Enter the lower and upper bound. The lower bound shall be a very negative number such as $-10^{9}$ . For the upper bound, enter

Enter the mean and standard deviation (or variance if required).Evaluate.

For example, on a Texas Instruments TI-84, evaluating $\text{normalcdf})(-1\text{E}99,\;13,\;11.2,\;2.1 )$ gives 0.804317 .

As a result,

$P(X\le 13) = 0.804317$ .

Number of green beans that are shorter than 13 centimeters:

Assume that the length of green beans for sale are independent of each other. The probability that each green bean is shorter than 13 centimeters is constant. As a result, the number of green beans out of 150 that are shorter than 13 centimeters follow a binomial distribution.

Number of trials

: 150.Probability of success

: 0.804317.

Let be the number of green beans out of this 150 that are shorter than 13 centimeters. $Y\sim\text{B}(150,0.804317)$ .

The expected value of a binomial random variable is the product of the number of trials and the probability of success on each trial. In other words,

$E(Y) = n\cdot p = 150 \times 0.804317 = 120.648\approx 121$

The expected number of green beans out of this 150 that are shorter than 13 centimeters will thus be approximately 121.

Answer from: Quest

step-by-step explanation:

Answer from: Quest

i think the answer is true

step-by-step explanation:

Another question on Mathematics

Mathematics, 21.06.2019 16:30

The weights of players in a basketball league are distributed normally. the distance (d) of each player's weight (w) from the mean of 86 kilograms was computed as follows: d = |w - 86| if d is greater than 7 for approximately 5% of the players, what is the approximate standard deviation of the players' weights? a. 1.75 kilograms b. 3.5 kilograms c. 4.3 kilograms d. 7 kilograms

Answers: 3

Answer

Mathematics, 21.06.2019 19:00

Jack did 3/5 of all problems on his weekend homework before sunday. on sunday he solved 1/3 of what was left and the last 4 problems. how many problems were assigned for the weekend?

Answers: 3

Answer

Mathematics, 22.06.2019 00:10

Me i need ! find the asymptote and determine the end behavior of the function from the graph. the asymptote of the function is= blank 1 . for very high x-values,y =blank 2 options for blank 1 x=2 x=-2 x=3 x=-3 blank 2 options moves towards negative infinity moves toward the horizontal asymptote moves toward the vertical asymptote moves toward positive infinity

Answers: 1

Answer

Mathematics, 22.06.2019 00:40

The formula for the volume of a right square pyramid is given below, where a is the side length of the base and h is the height.

Answers: 1

Answer

You know the right answer?

Correct answer only !

use technology or a z-score table to answer the question.

Questions

Mathematics, 29.01.2020 15:02

Uncle drew scored 282828 points in 5\dfrac565 6 5 5, start fraction, 5, divided by, 6, end fraction minutes during a game of baske...