Question

a media statistics agency reports that the mean number of televisions in a household in a particular country is 2.24. assume that the population standard deviation number of television sets in this country is 1.38.

Answer 1

The probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

Given: Mean(μ) = 2.24, Standard deviation(σ) = 1.38, Sample size(n) = 1.28 and a random variable for X = 2.55

What is a probability distribution?

A probability distribution is a kind of function for a discrete variable X, whose distribution over a certain interval is discrete or it shows the density of a random variable X that occurs over a given interval in the given distribution.

What is the z-score?

The z-score or the z-value shows the number of standard deviations unit away lies the given random variable from the mean.

Or it shows how dense is the value for a random variable near or away from the mean.

The formula to calculate the z-score from the mean. The standard deviation is:

z = (X - μ) / ( σ / √(n)) where,

z = z-score,

X = random variable,

μ = mean,

σ = standard deviation, and

n = sample size

Let's solve the given question:

We have,

Mean(μ) = 2.24,

Standard deviation(σ) = 1.38,

Sample size(n) = 1.28, and

a random variable for X = 2.55

As it is given sample means at least 2.55 so we have to find the Z(x ≥ 2.55).

Therefore, Z(x ≥ 2.55) = (2.55 - μ) / ( σ / √(n))

Substituting all values we get:

Z(x ≥ 2.55) = (2.55 - 2.24) / ( 1.38 / √(40))

Z(x ≥ 2.55) = 0.01 / 0.21819

Z(x ≥ 2.55) = 0.48173

Hence the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household is 0.48173.

Know more about “probability distribution” here: brainly.com/question/11234923

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Disclaimer: The given question is incomplete. The complete question is mentioned below:

a media statistics agency reports that the mean number of televisions in a household in a particular country is 2.24 with a standard deviation of 1.38 what is the probability of a random sample of 40 households having a sample means a number of at least 2.55 televisions per household?