Respuesta :
The probability that a simple random sample of 45 unemployed individuals will provide is 0.7372
Here, μ = 17.5, σ = 0.8944, x1 = 16.5 and x2 = 18.5.
We need to compute P(16.5<= X <= 18.5).
The corresponding z-value is calculated using Central Limit Theorem.
z = (x - μ)/σ
z1 ⇒ (16.5 - 17.5)/0.8944 = -1.12
z2 ⇒ (18.5 - 17.5)/0.8944 = 1.12
Therefore, we get
P(16.5 <= X <= 18.5) = P((18.5 - 17.5)/0.8944) <= z <= (18.5 - 17.5)/0.8944)
⇒ P(-1.12 <= z <= 1.12) = P(z <= 1.12) - P(z <= -1.12)
⇒ 0.8686 - 0.1314 = 0.7372
The principal limit theorem states that if you have a population with imply μ and trendy deviation σ and take sufficiently huge random samples from the populace with alternative, then the distribution of the pattern method may be about usually distributed.
The relevant limit theorem (CLT) states that the distribution of pattern manner approximates a normal distribution as the pattern size gets larger, regardless of the population's distribution. sample sizes identical to or extra than 30 are often considered enough for the CLT to preserve.
Learn more about the central limit theorem here https://brainly.com/question/18403552
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