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adelina 88 [10]
3 years ago
14

Assume the random variable X is normally distributed with mean mu equals 50 and standard deviation sigma equals 7. Compute the p

robability. Be sure to draw a normal curve with the area corresponding to the probability shaded.

Mathematics
1 answer:
drek231 [11]3 years ago
6 0

Answer:

The probability that <em>X</em> is less than 42 is 0.1271.

Step-by-step explanation:

The random variable <em>X </em>follows a Normal distribution.

The mean and standard deviation are:

E (X) = <em>μ</em> = 50.

SD (X) = <em>σ</em> = 7.

A normal distribution is continuous probability distribution.

The Normal probability distribution with mean µ and standard deviation σ is given by,

f_{X}(\mu, \sigma)=\frac{1}{\sigma\sqrt{2\pi}}e^{-(x-\mu)^{2}/2\sigma^{2}};\ -\infty

To compute the probability of a Normal random variable we first standardize the raw score.

The raw scores are standardized using the formula:

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

These standardized scores are known as <em>z</em>-scores and they follow normal distribution with mean 0 and standard deviation 1.

Compute the probability of (X < 42) as follows:

P(X

*Use a <em>z</em>-table for the probability.

Thus, the probability that <em>X</em> is less than 42 is 0.1271.

The normal curve is shown below.

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Answer:

11%

Step-by-step explanation:

The full circle graph represents 100% of the given population. All populations are given except for "three or more." Adding all percentages of each population should add up to 100%.

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Two absences: 21%

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

Given;

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Make a sketch of the problem as follows;

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Therefore, the height of the tree is 19.2 ft

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3 years ago
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