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An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and

egoroff_w [7]

Answer:

a) $P(140$

$P(0.036$

b) $P(140< \bar X$

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

Part a

Let X the random variable that represent the weights of a population, and for this case we know the distribution for X is given by:

$X \sim N(139,28.1)$

Where $\mu=139$ and $\sigma=28.1$

We are interested on this probability

$P(140$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(140$

And we can find this probability like this:

$P(0.036$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(0.036$

Part b

For this case we select a sample size of n =32. Since the distribution for X is normal then the distribution for the sample mean $\bar X$ is given by:

$\bar X \sim N(\mu=139, \frac{\sigma}{\sqrt{n}}=\frac{28.1}{\sqrt{32}}=4.97)$

And the new z score would be:

$Z=\frac{\bar X -\mu}{\sigma_{\bar x}}$

$P(140< \bar X$

5 0

2 years ago

Esma has a box that is 20 cm wide 10 cm high, and 10 cm deep she wants to fill the box with packages that are 5 cm wide 2 cm hig

anastassius [24]

Answer:

Esma can fit 3 packages in the box because 20+10+10=30 and 5+2+2=9 so if you add up 9 three times you get 27 and that is the closest number you can get before going over.

Step-by-step explanation:

6 0

2 years ago

What is the y-intercept of the function, and what does this tell you about the car?

scZoUnD [109]

Write an equation in the standard form to represent the total rent (y) that Sam has to ... is the y-intercept of the function, and what does this tell you about the car?

6 0

3 years ago

- How do I solve this,I do not know how to start it

Ulleksa [173]

Answer:

what do you mean?

Step-by-step explanation:

5 0

2 years ago

On Triangle ABC, Angle A measures 30 degrees, Angle B measures 90 degrees, and Angle C measures 60 degrees. List the sides of Tr

Mazyrski [523]

Answer:

A=30 B=90 C=60

Step-by-step explanation:

A=30 C=60 B=90

8 0

3 years ago