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?
