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KonstantinChe [14]
3 years ago
12

Over 1,000 people try to climb Mt. Everest every year. Of those who try to climb Everest, 31 percent succeed. The probability th

at a climber is at least 60 years old is 0.04. The probability that a climber is at least 60 years old and succeeds in climbing Everest is 0.005.
Mathematics
1 answer:
Arada [10]3 years ago
3 0

Answer:

A. P(success/age≥60) = 12.5%

B. Yes, the success is independent of age.

Step-by-step explanation:

Probability of success, given that a climber is at least 60 years old is calculated using conditional probability rule

P(A|B) = P(A n B)/P(B)

Probability of success given that a climber is at least 60 years old is given by

P(success|age≥60) = P(success n age ≥ 60)/P(age ≥ 60) = 0.005/0.04

= 0.125

P(success|age≥60) = 12.5%

B. The success is independent on age

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A Government company claims that an average light bulb lasts 270 days. A researcher randomly selects 18 bulbs for testing. The s
Fofino [41]

Answer:

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use 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.

For a proportion p in a sample of size n, the sampling distribution of the sample proportion will be approximately normal with mean \mu = p and standard deviation s = \sqrt{\frac{p(1-p)}{n}}

In this question, we have that:

\mu = 270, \sigma = 90, n = 18, s = \frac{90}{\sqrt{18}} = 21.2

What is the probability that 18 randomly selected bulbs would have an average life of no more than 260 days?

This is the pvalue of Z when X = 260. So

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

By the Central Limit Theorem

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

Z = \frac{260 - 270}{21.2}

Z = -0.47

Z = -0.47 has a pvalue of 0.3192.

31.92% probability that 18 randomly selected bulbs would have an average life of no more than 260 days

5 0
3 years ago
Wyatt uses 3.15 cups of flour in a recipe that makes 9 shortcakes. Cora uses 2.4 cups of flour in a recipe that makes 8 shortcak
dalvyx [7]
For Wyatt's recipe the rate is:
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 r1 = 0.35
 For Cora's recipe the rate is:
 r2 = 2.4 / 8
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0.05 cups of flour per shortcake less is needed for Cora's recipe
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A number that can be written as a fraction?
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Answer:

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