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Rudiy27
3 years ago
8

The mean cost for a pint of frozen yogurt is $1.50, with a standard deviation of $0.10.

Mathematics
1 answer:
djverab [1.8K]3 years ago
6 0

Answer:

The correct answer is:

0.01$ (c)

Step-by-step explanation:

Standard deviation is a measure of how spread out numbers are from the mean value. The formula for standard deviation is given by:

s = \sqrt{\frac{\sum(x - \bar x)}{n} } \\where:\\x = sample\ \\\bar x\ = mean\\n\ = number\ of\ samples\

Variance is a measure of the squared differences from the mean.

Variance is simply the square of the standard deviation. It is mathematically shown as:

s^2 = \frac{\sum(x - \bar x)}{n} }

Now in our example,

Stabnard deviation = $0.10

Variance = (standard deviation)²

Variance = (0.10)²

Variance = $0.01

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2 years ago
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There are 4 people at a party. Consider the random variable X=’number of people having the same birthday ’ (match only month, N=
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Answer:

S = {0,2,3,4}

P(X=0) = 0.573 , P(X=2) = 0.401 , P(x=3) = 0.025, P(X=4) = 0.001

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Step-by-step explanation:

Let the number of people having same birth month be = x

The number of ways of distributing the birthdays of the 4 men = (12*12*12*12)

The number of ways of distributing their birthdays = 12⁴

The sample space, S = { 0,2,3,4} (since 1 person cannot share birthday with himself)

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P(X=0) = 0.573

P(X=2) = P(2 months are common) P(1 month is common, 1 month is not common)

P(X=2) = \frac{3C2 * 12P2}{12^{4} } + \frac{4C2 * 12P3}{12^{4} }

P(X=2) = 0.401

P(X=3) = \frac{4C3 * 12P2}{12^{4} }

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P(X=4) = \frac{12}{12^{4} }

P(X=4) = 0.001

Mean, \mu = \sum xP(x)

\mu = (0*0.573) + (2*0.401) + (3*0.025) + (4*0.001)\\\mu = 0.879

Standard deviation, SD = \sqrt{\sum x^{2} P(x) - \mu^{2}}  \\SD =\sqrt{ [ (0^{2} * 0.573) + (2^{2}  * 0.401) + (3^{2} * 0.025) + (4^{2} * 0.001)] - 0.879^{2}}

SD = 1.033

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