Answer :
The probability of a random sample of 80 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
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) = 80, 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 / √(80))
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.
learn more about of “probability distribution” here: brainly.com/question/11234923
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