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mote1985 [20]
3 years ago
15

The monthly salary of all adults in a certain US town is known to be right skewed with a mean of $3700. If a random sample of si

ze 40 adults were selected from that town, what would be the shape of the distribution of the sample mean?
Mathematics
1 answer:
Alexxandr [17]3 years ago
7 0

Answer:

The shape of the distribution of the sample mean would be bell-shaped(normally distributed).

Step-by-step explanation:

The Central Limit Theorem answers this question.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size, of at least 30, can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}.

In this problem, we have that

The population distribution is right-skewed.

Sampling distribution of the sample mean with size 40.

The Central Limit Theorem estabilishes that the sampling distribution of the sample mean will be normally distributed, even if the distribution of the population is not.

So the shape of the distribution of the sample mean would be bell-shaped(normally distributed).

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Suppose a couple planned to have three children. Let X be the number of girls the couple has.
sesenic [268]

Answer:

a) {GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

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Step-by-step explanation:

We are given the following in the question:

Suppose a couple planned to have three children. Let X be the number of girls the couple has.

a) possible arrangements of girls and boys

Sample space:

{GGG, GGB, GBG, BGG, BBG, BGB, GBB, BBB}

b) sample space for X

X is the number of girls couple has. Thus, X can take the values 0, 1, 2 and 3 that is 0 girls, 1 girl, 2 girls and three girls from three children.

Sample space: {0,1,2,3}

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That is we have to compute the probability that couple has exactly two girls.

\text{Probability} = \displaystyle\frac{\text{Number of favourable outcomes}}{\text{Total number of outcomes}}

Favorable outcome: {GGB, GBG, BGG}

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