Respuesta :
The Probability of the sample mean differing from the true mean by more than 1.4 dollars = 0.8584
What do you mean by Probability?
The degree to which something is likely; the probability that something will occur or will be the case:(1): the likelihood that a specific event will occur (2): the proportion of conceivable outcomes to the number of outcomes in an exhaustive set of equally likely options that result in a specific event. A field of mathematics that focuses on the investigation of probability2: something that is likely to happen (such as an event or circumstance)3: the characteristic or state of being likely
According to the given information:
From this population, a sample of size n = 54 is drawn.
Let [tex]\bar x[/tex] be the mean of sample.
The sampling distribution of the [tex]\bar x[/tex] is approximately normal with
Mean (μ[tex]_\bar x[/tex]) = μ = 42
SD (σ[tex]_\bar x[/tex]) = n = 7
√(54)= 0.95257934441
Find P([tex]\bar x[/tex] The differ from the true mean by less than 1.4)
= P([tex]\bar x[/tex] The differ from 42 by less than 1.4)
= P(42 - 1.4 < [tex]\bar x[/tex] < 42 + 1.4 )
= P( 40.6 < [tex]\bar x[/tex] < 19853)
= P ([tex]\bar x[/tex] < 43.4) - P([tex]\bar x[/tex] < 40.6)
= P[(T - μ[tex]_\bar x[/tex]) /σ[tex]_\bar x[/tex] < (43.4 -42 )/0.95257934441] - P[(T - μ[tex]_\bar x[/tex]) /σ[tex]_\bar x[/tex] < (40.6 -42 )/0.95257934441]
= P(Z < 1.47) - P(Z < - 1.47)
= 0.9292 - 0.0708.. (use z table)
= 0.8584
The likelihood of the sample mean differing from the true mean by more than 1.4 dollars = 0.8584
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