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laila [671]
3 years ago
13

The safety officers of a mining company take an SRS of 500500500 employees and finds that 15\, percent of the sampled employees

wear contact lenses. The safety officers may take several more samples like this. Suppose it is really 12\, percent of the approximately 34{,}00034,00034, comma, 000 employees in the company who wear contact lenses. What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses
Mathematics
1 answer:
RideAnS [48]3 years ago
7 0

Answer:

The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.

Step-by-step explanation:

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}}

12% of the employees wear contact lenses.

This means that p = 0.12

Samples of 500:

This means that n = 500

What are the mean and standard deviation of the sampling distribution of the proportion of employees who wear contact lenses?

Mean:

\mu = p = 0.12

Standard deviation:

s = \sqrt{\frac{p(1-p)}{n}} = \sqrt{\frac{0.12*0.88}{500}} = 0.0145

The mean of the sampling distribution of the proportion of employees who wear contact lenses is 0.12 and the standard deviation is 0.0145.

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The interval of 95% confidence, for normally distributed variables, is average +/- 2 * standard deviation:

(-2*standard deviation + average , average + 2*standard deviation)

(-2*18 + 62.5 , 2*18 + 62.5) = (-36 + 62.5 , 36 + 62.5) = (26.5 , 98.5)

Answer: option D)


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3 years ago
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Answer:

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HELPPPPP! Tamlin collects action figures and has 2 more female action figures than male action figures. He chooses two action fi
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Answer:

x+2/2(2x+1)

Step-by-step explanation:

Tamlin has x male action figures and x + 2 female action figures, so a total of x + x + 2, or 2x + 2 action figures. The probability of picking two female action figures without replacement is equal to the product of the probability of

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The probability of picking 1 female action figure from the total is equal to the total number of female action figures divided by the total number of action figures.

The probability of picking 1 female action figure after 1 has been removed is equal to the total number of female action figures minus 1 divided by the total number of action figures minus 1.

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Put the following equation of a line into slope-intercept form, simplifying all
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8 0
3 years ago
Plz help I do not understand
erastovalidia [21]

Answer:

-128

Step-by-step explanation:

When it says that x = a number, it means you just need to plug in that number for x in the equation. So in this case, we'd plug in -12 and get:

y = -200-6(-12)

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y= -200+72

Add, and our final answer is:

y=-128

Hopefully this helped, and if I was correct, I'd appreciate it if you marked me as the Brainliest :)

5 0
3 years ago
Read 2 more answers
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