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lutik1710 [3]
3 years ago
15

The probability that a randomly selected​ 5-year-old male horned beetle will live to be 6 years old is 0.25624.​

Mathematics
2 answers:
dalvyx [7]3 years ago
8 0

Answer:

(a) The probability that two randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is 0.06566.

(b) The probability that six randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is 0.000283.

Step-by-step explanation:

It is given that the probability that a randomly selected​ 5-year-old male horned beetle will live to be 6 years old is 0.25624.​

(a)

We need to find the probability that two randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old.

P=0.25624\times 0.25624=(0.25624)^2=0.0656589376\approx 0.06566

Therefore the probability that two randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is 0.06566.

(b)

We need to find the probability that six randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old.

P=0.25624\times 0.25624\times 0.25624\times 0.25624\times 0.25624\times 0.25624=(0.25624)^6=0.000283061988948\approx 0.000283

Therefore the probability that six randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is 0.000283.

Vadim26 [7]3 years ago
7 0

Answer: (a)  0.0656

(b) 0.00028

Step-by-step explanation:

Since we have given that

Probability that a randomly selected 5-year old male horned beetle will live to be 6 years old = 0.25624

If there are

Number of male horned beetles = 2

So, probability that two randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is given by

(0.25624)^2\\\\=0.0656

If number of male horned beetles = 6

So, probability that six randomly selected​ 5-year-old male horned beetles will live to be 6 years​ old is given by

(0.25624)^6\\\\=0.00028\\

Hence, (a)  0.0656

(b) 0.00028

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Answer:

Domain: x ≥ 0

Range: All real numbers

Step-by-step explanation:

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This means only the x values of 0 and greater are used in the function. Since the domain is the set of all x values then it is x≥0.

This also means that all y values are used on the y-axis. There is no restriction on the y values. Since the range is the set of all y values then it is all real numbers.

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3 years ago
A certain cold remedy has an 88% rate of success of reducing symptoms within 24 hours. Find the probability that in a random sam
Hitman42 [59]

Answer:

The probability of cured people in who took the remedy is 8/9.

Step-by-step explanation:

Success rate of the cold remedy = 88%

The number of people who took the remedy = 45

Now, 88% of 45 = \frac{88}{100}  \times 45 = 39.6

and 39.6 ≈ 40

So, out of 45 people, the remedy worked on total 40 people.

Now, let E: Event of people being cured by cold remedy

Favorable outcomes = 40

\textrm{Probability of Event E}  = \frac{\textrm{Total number of favorable outcomes}}{\textrm{Total outcomes}}

or, \textrm{Probability of people getting cured}  = \frac{\textrm{40}}{\textrm{45}}  = \frac{8}{9}

Hence, the probability of cured people in who took the remedy is 8/9.

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Find the value of x to the nearest degree <br>a. 30<br>b. 60<br>c. 70<br>d. 85
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The overhead reach distances of adult females are normally distributed with a mean of 197.5 cm197.5 cm and a standard deviation
fiasKO [112]

Answer:

a) 5.37% probability that an individual distance is greater than 210.9 cm

b) 75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c) Because the underlying distribution is normal. We only have to verify the sample size if the underlying population is not normal.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

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

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value 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. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean \mu and standard deviation \sigma, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean \mu and standard deviation s = \frac{\sigma}{\sqrt{n}}.

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

In this question, we have that:

\mu = 197.5, \sigma = 8.3

a. Find the probability that an individual distance is greater than 210.9 cm

This is 1 subtracted by the pvalue of Z when X = 210.9. So

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

Z = \frac{210.9 - 197.5}{8.3}

Z = 1.61

Z = 1.61 has a pvalue of 0.9463.

1 - 0.9463 = 0.0537

5.37% probability that an individual distance is greater than 210.9 cm.

b. Find the probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

Now n = 15, s = \frac{8.3}{\sqrt{15}} = 2.14

This probability is 1 subtracted by the pvalue of Z when X = 196. Then

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

By the Central Limit Theorem

Z = \frac{X - \mu}{s}

Z = \frac{196 - 197.5}{2.14}

Z = -0.7

Z = -0.7 has a pvalue of 0.2420.

1 - 0.2420 = 0.7580

75.80% probability that the mean for 15 randomly selected distances is greater than 196.00 cm.

c. Why can the normal distribution be used in part​ (b), even though the sample size does not exceed​ 30?

The underlying distribution(overhead reach distances of adult females) is normal, which means that the sample size requirement(being at least 30) does not apply.

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LUCKY_DIMON [66]
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and has a determinant of

\det\mathbf J=-\dfrac{2x}y

Note that we need to use the Jacobian in the other direction; that is, we've computed

\mathbf J=\dfrac{\partial(u,v)}{\partial(x,y)}

but we need the Jacobian determinant for the reverse transformation (from (x,y) to (u,v). To do this, notice that

\dfrac{\partial(x,y)}{\partial(u,v)}=\dfrac1{\dfrac{\partial(u,v)}{\partial(x,y)}}=\dfrac1{\mathbf J}

we need to take the reciprocal of the Jacobian above.

The integral then changes to

\displaystyle\iint_{\mathcal W_{(x,y)}}e^{xy}\,\mathrm dx\,\mathrm dy=\iint_{\mathcal W_{(u,v)}}\dfrac{e^u}{|\det\mathbf J|}\,\mathrm du\,\mathrm dv
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