College

Suppose the horses in a large stable have a mean weight of 992 lbs and a standard deviation of 141 lbs. What is the probability that the mean weight of a sample of horses would differ from the population mean by less than 13 lbs if 37 horses are sampled at random from the stable?

Round your answer to four decimal places.

Answer :

Answer:

[tex]P(\overline{x}>1123) =P(z>5.65)=0[/tex]

Step-by-step explanation:

Here [tex]\mu=992 and \sigma=141[/tex]

We need to find [tex]P(\overline{x}>1123) for n=37[/tex]

As n=36>30, as per central limit theorem, distribution of [tex]\overline{x}[/tex] is normal with [tex]\mu=992 and \sigma=\frac{\sigma}{\sqrt{n}}=\frac{141}{\sqrt{37}}=23.18[/tex]

Now [tex]P(\overline{x}>1123) =P(z>\frac{1123-992}{23.18})[/tex]

[tex]P(\overline{x}>1123) =P(z>5.65)=0[/tex]

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