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Iteru [2.4K]
3 years ago
13

A population of values has a normal distribution with μ = 247 and σ = 62.2. You intend to draw a random sample of size n = 16. (

a) Find the probability that a single randomly selected value is greater than 295.2. (b) Find the probability that a sample of size n= 16 is randomly selected with a mean greater than 295.2. Give your answers as numbers accurate to 4 decimal places. Answers obtained using exact z-scores or z-scores rounded to 3 decimal places are accepted.
Mathematics
1 answer:
nadya68 [22]3 years ago
8 0

Answer:

a) z = \frac{295.2-247}{62.2}=0.772

And using the normal distribution table or excel we got:

P(Z>0.772) = 1-P(Z

b) z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119

And we can use the normal standard table or excel in order to find the probability and we got:

P(z>3.119) =1-P(Z

Step-by-step explanation:

For this case we know that the random variable of interest is normally distributed with the following parameters:

X \sim N (\mu = 247, \sigma =62.2)

Part a

We want to find this probability:

P(X>295.2)

And we can use the z score formula given by:

z = \frac{X-\mu}{\sigma}

Replacing we got:

z = \frac{295.2-247}{62.2}=0.772

And using the normal distribution table or excel we got:

P(Z>0.772) = 1-P(Z

Part b

We select a random sample of size n = 16 and we try to find this probability:

P(\bar X >295.2)

And we can use the z score formula given by:

z = \frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}

And replacing we got:

z = \frac{295.5 -247}{\frac{62.2}{\sqrt{16}}}= 3.119

And we can use the normal standard table or excel in order to find the probability and we got:

P(z>3.119) =1-P(Z

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Answer:

y=-\dfrac{5}{3}x+6.5

Step-by-step explanation:

Given: trapezoid RSTU with vertices R(-1, 5), S(1, 8), T(7, -2), and U(2, 0).

Plot these points on the coordinate plane. As you can see, lines RU and ST are parallel lines and segments ST and RU are bases of the trapezoid.

The median of the trapezoid (the middle line) passes through the midpoints of the sides RS and TU. Find these midpoints:

M\left(\dfrac{x_S+x_R}{2},\dfrac{y_S+y_R}{2}\right)\Rightarrow M(0,6.5)\\ \\N\left(\dfrac{x_T+x_U}{2},\dfrac{y_T+y_U}{2}\right)\Rightarrow N(4.5,-1)

The equation of the line MN is

\dfrac{x-0}{4.5-0}=\dfrac{y-6.5}{-1-6.5}\\ \\\dfrac{x}{4.5}=\dfrac{y-6.5}{-7.5}\\ \\y=-\dfrac{5}{3}x+6.5

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Answer:

The key to this question is converting all the mass units to the same unit and adding them all up.

The only value that isn't consistent with the other units is 450 gm or grams.

Recall that 1 gram is equal to 0.001 kilo grams. So if you want to convert grams to kilograms you would multiply that amount by 0.001 or 1/1000

450gm * \frac{1}{1000} = 0.45kg

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53.6kg + 0.45kg + 4.5kg = 58.55 kg\\

(Now a few footnotes here, that I considered but wasn't sure about. The answer asks for weight, but you're only given mass to work with. That would be fine, if the question asked you to convert it to SI weight units like Newtons, but there's no mention of that. And also I'm not sure if the question requires significant digits. But I'll continue the answer if you think so)

To convert this into weight in Newtons, multiply by 9.81 m/s^2

58.55kg*9.81m/s^2 = 574.3755 N\\\\= 5.7 * 10^2 N

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