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xeze [42]
2 years ago
13

How long is a bus journey that starts at 8.55 a.m. and ends at 9.17 a.m.?

Mathematics
1 answer:
vladimir1956 [14]2 years ago
6 0

Answer:

5+17=22 minute

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A normally distributed population has mean 57,800 and standard deviation 750. Find the probability that a single randomly select
Stels [109]

Answer:

(a) Probability that a single randomly selected element X of the population is between 57,000 and 58,000 = 0.46411

(b) Probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = 0.99621

Step-by-step explanation:

We are given that a normally distributed population has mean 57,800 and standard deviation 75, i.e.; \mu = 57,800  and  \sigma = 750.

Let X = randomly selected element of the population

The z probability is given by;

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

(a) So, P(57,000 <= X <= 58,000) = P(X <= 58,000) - P(X < 57,000)

P(X <= 58,000) = P( \frac{X-\mu}{\sigma} <= \frac{58000-57800}{750} ) = P(Z <= 0.27) = 0.60642

P(X < 57000) = P( \frac{X-\mu}{\sigma} < \frac{57000-57800}{750} ) = P(Z < -1.07) = 1 - P(Z <= 1.07)

                                                          = 1 - 0.85769 = 0.14231

Therefore, P(31 < X < 40) = 0.60642 - 0.14231 = 0.46411 .

(b) Now, we are given sample of size, n = 100

So, Mean of X, X bar = 57,800 same as before

But standard deviation of X, s = \frac{\sigma}{\sqrt{n} } = \frac{750}{\sqrt{100} } = 75

The z probability is given by;

           Z = \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)  

Now, probability that the mean of a sample of size 100 drawn from this population is between 57,000 and 58,000 = P(57,000 < X bar < 58,000)

P(57,000 <= X bar <= 58,000) = P(X bar <= 58,000) - P(X bar < 57,000)

P(X bar <= 58,000) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } <= \frac{58000-57800}{\frac{750}{\sqrt{100} } } ) = P(Z <= 2.67) = 0.99621

P(X < 57000) = P( \frac{Xbar-\mu}{\frac{\sigma}{\sqrt{n} } } < \frac{57000-57800}{\frac{750}{\sqrt{100} } } ) = P(Z < -10.67) = P(Z > 10.67)

This probability is that much small that it is very close to 0

Therefore, P(57,000 < X bar < 58,000) = 0.99621 - 0 = 0.99621 .

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The answer is D. 2n + 1
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Given the triangle below,what is the length of the hypotenuse
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Hypotenuse = 9cm^2+ 13cm^2
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Simplify.<br> 3 1<br> 8 8<br> OA)<br> 2<br> 1<br> B)<br> 2<br> C)<br> OD)<br> 8
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Hello Love!! ♡ 

»»————-  \red{Answer\:} ————-««

\Huge{\boxed{\frac{1}{4}}}

☆♬○♩●♪✧♩ \bold{EXPLANATION\;} ♩✧♪●♩○♬☆

\mathfrak{apply~the~fraction~rule~:}~\frac{a}{c}~ -~\frac{b}{c} = \frac{a~-~b}{c}

= \frac{3-1}{8}

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\mathfrak{cancel~the~numbers~:}~\frac{2}{8} = \frac{1}{4}

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Answer~:

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