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JulsSmile [24]
3 years ago
10

Assume that different groups of couples use the XSORT method of gender selection and each couple gives birth to one baby. The XS

ORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5. Now consider a group consisting of 36 couples. a.) Find the mean and standard deviation for the numbers of girls in groups of 36 births
Mathematics
1 answer:
olganol [36]3 years ago
3 0

Answer:

Mean and Standard deviation for the numbers of girls in groups of 36 births are 18 and 3 respectively.

Step-by-step explanation:

We are given that he X SORT method is designed to increase the likelihood that a baby will be a girl, but assume that the method has no effect, so the probability of a girl is 0.5.

Now consider a group consisting of 36 couples.

The above situation can be represented through binomial distribution;

P(X=r)=\binom{n}{r} \times p^{r} \times (1-p)^{n-r} ;x=0,1,2,3,.....

where, n = number of trials (samples) taken = 36 couples

            r = number of success

            p = probability of success which in our question is probability

                   of a girl, i.e.; p = 0.5

<em><u>Let X = Numbers of girls in groups of 36 births </u></em>

So, X ~ Binom(n = 36, p = 0.5)

Now, mean for the numbers of girls in groups of 36 births is given by;

         <u>Mean</u>, E(X) = n \times p = 36 \times 0.5 = 18

Also, standard deviation for the numbers of girls in groups of 36 births is given by;

        <u>Standard deviation</u>, S.D.(X) =  \sqrt{n\times p\times (1-p)}

                                                      =  \sqrt{36\times 0.5\times (1-0.5)}

                                                      =  3

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Step-by-step explanation:

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Answer:

56.96% probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits

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 single player:

\mu = 355, \sigma = 80

For the sample mean(of 48 playes).

n = 48, s = \frac{80}{\sqrt{48}} = 11.547

What is the probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits?

This is the pvalue of Z when X = 360 subtracted by the pvalue of Z when X = 340. So

X = 360

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

By the Central Limit Theorem

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

Z = \frac{360 - 355}{11.547}

Z = 0.43

Z = 0.43 has a pvalue of 0.6664

X = 340

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

Z = \frac{340 - 355}{11.547}

Z = -1.30

Z = -1.30 has a pvalue of 0.0968

0.6664 - 0.0968 = 0.5696

56.96% probability on a randomly selected team of 48 players that the average number of head hits per player is between 340 and 360 hits

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barxatty [35]

Answer:

A

Step-by-step explanation:

Khan gives you right answer and tells you what's wrong, but this site is for help so, all you need to do is use the destructive property.

12 x 2= 24 12 x 3 = 36 12 x -1 = -12

now you have the original expression, 24 + 36 - 12 (without the letters.)

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