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Vika [28.1K]
3 years ago
10

The average weight of a chicken egg is 2.25 ounces with a standard deviation of 0.2 ounces. You take a random sample of a dozen

eggs. What is the probability that the mean weight of the eggs in the sample will be less than 2.2 ounces?
Mathematics
1 answer:
n200080 [17]3 years ago
5 0

Answer:

P(\bar X

P(\bar X

Step-by-step explanation:

Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  

Let X the random variable that represent interest on this case, and for this case we know the distribution for X is given by:

X \sim N(\mu,\sigma)  

And let \bar X represent the sample mean, the distribution for the sample mean is given by:

\bar X \sim N(\mu,\frac{\sigma}{\sqrt{n}})

On this case  \bar X \sim N(2.25,\frac{0.2}{\sqrt{12}})

Solution to the problem

We want this probability:

P(\bar X

The best way to solve this problem is using the normal standard distribution and the z score given by:

z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}

If we apply this formula to our probability we got this:

P(\bar X

P(\bar X

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