For the population of one town, the number of siblings, x, is a random variable whose relative frequency histogram has a reverse J-shape. The mean number of siblings is 1.3 and the standard deviation is 1.4. Let denote the mean number of siblings for a random sample of size 30. Determine the sampling distribution of the mean for samples of size 30, and give its mean and standard deviation

The mean is given by:

And the deviation is given by:

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".  

Solution to the problem

Let X the random variable that represent the number of siblings of a population, and for this case we know the distribution for X is given by:

Where and

The sample mean is given by this formula:

The sample size is n =30, and the distribution for the sample mean is given by:

The mean is given by:

And the deviation is given by:

i can answer this question sweetie!

step-by-step explanation:

option a, c,d are correct.

step-by-step explanation:

from the given figure, it is given that z is equidistant from the sides of the triangle rst, then from triangle tzb and triangle szb, we have

tz=sz(given)

bz=zb(common)

therefore, by rhs rule,δtzb ≅δszb

by cpctc, sz≅tz

also, from δctz and δasz,

tz=sz(given)

∠tcz=∠saz(90°)

by rhs rule, δctz ≅ δasz, therefore by cpctc, ∠ctz≅∠asz

also,from δasz and δzsb,

zs=sz(common)

∠zbs=∠saz=90°

by rhs rule, δasz ≅δzsb, therefore, by cpctc, ∠asz≅∠zsb

hence, option a, c,d are correct.