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2 years ago

Homework:Section 5.3 Homework

1 answer:

8 0

The probability that all three components fail is 1.756 × 10⁻⁷. The probability of at least one of the components does not fail 0.9999998244.

<h3>What is a Probability?</h3>

Probability is the likelihood for an event to occur. In a given statistical distribution, the probability explains the range of values and probabilities that a randomized variable could have.

From the given information;

Assuming each component's failure/success is independent of the others: the probability that all three components fail is:

P(three components fail) = (0.0056)^3

P(three components fail) = 1.756 × 10⁻⁷

The probability that at least one does not fail is:

P(at least one does not fail) = 1 - P(all three components fail)

P(at least one does not fail) = 1 - 1.756 × 10⁻⁷

P(at least one does not fail) = 0.9999998244

Learn more about probability here:

brainly.com/question/24756209

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If a jar of coins contain 20 half dollars and 160 quarters what is the monetary value of coins?

saul85 [17]

Hello!

Half dollar = 0.50 cents

Quarter = 0.25 cents

20 ÷ 2 = 10

160 ÷ 4 = 40 br />
40 + 10 = 50

ANSWER:
The monetary value of the coins is $50.00.

3 0

3 years ago

Time spent using e-mail per session is normally distributed, with mu equals 11 minutes and sigma equals 3 minutes. Assume that

liq [111]

Answer:

a) 0.259

b) 0.297

c) 0.497

Step-by-step explanation:

To solve this problem, it is important to know 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 random variable X, with mean $\mu$ and standard deviation $\sigma$ , a large sample size can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$

In this problem, we have that:

$\mu = 11, \sigma = 3$

a. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 25, s = \frac{3}{\sqrt{25}} = 0.6$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.6}$

$Z = 0.33$

$Z = 0.33$ has a pvalue of 0.6293.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.6}$

$Z = -0.33$

$Z = -0.33$ has a pvalue of 0.3707.

0.6293 - 0.3707 = 0.2586

0.259 probability, rounded to three decimal places.

b. If you select a random sample of 25 sessions, what is the probability that the sample mean is between 10.5 and 11 minutes?

Subtraction of the pvalue of Z when X = 11 subtracted by the pvalue of Z when X = 10.5. So

X = 11

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

$Z = \frac{11 - 11}{0.6}$

$Z = 0$

$Z = 0$ has a pvalue of 0.5.

X = 10.5

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

$Z = \frac{10.5 - 11}{0.6}$

$Z = -0.83$

$Z = -0.83$ has a pvalue of 0.2033.

0.5 - 0.2033 = 0.2967

0.297, rounded to three decimal places.

c. If you select a random sample of 100 sessions, what is the probability that the sample mean is between 10.8 and 11.2 minutes?

Here we have that $n = 100, s = \frac{3}{\sqrt{100}} = 0.3$

This probability is the pvalue of Z when X = 11.2 subtracted by the pvalue of Z when X = 10.8.

X = 11.2

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

By the Central Limit Theorem

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

$Z = \frac{11.2 - 11}{0.3}$

$Z = 0.67$

$Z = 0.67$ has a pvalue of 0.7486.

X = 10.8

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

$Z = \frac{10.8 - 11}{0.3}$

$Z = -0.67$

$Z = -0.67$ has a pvalue of 0.2514.

0.7486 - 0.2514 = 0.4972

0.497, rounded to three decimal places.

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3 years ago

There are 154 males and i36 females participating in a marathon. What percent of the particpants are male?

lilavasa [31]

Answer:

154 im pretty sure sorry if wrong Q^Q

Step-by-step explanation:

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3 years ago

Tamara wants to buy a tablet that costs $437. She saves $50 a month for 9 months. Does she have enough money to buy the tablet?

satela [25.4K]

Answer:

Yes, because 50 • 9 = 450 and 450 is greater than 437.

50 • 9 = 450 > 437

Step-by-step explanation:

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3 years ago

(Please help, I will mark brainliest to the most accurate answer)

Minchanka [31]

Answer:

r=41/2

Step-by-step explanation:

The radius of a circle is always half it's diameter. In this circle, the diameter is 41 centimeters, so the radius would be half of that- which is 41/2 or 20.5 cm.

Hope this helps!

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3 years ago

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