Question

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the average number of moves a person makes in his or her lifetime is 12 and the standard deviation is 3.5. assume that the sample is taken from a large population and the correction factor can be ignored. use la tabla de distribución normal estándar. round the final answers to four decimal places and intermediate z value calculations to two decimal places.
parte 1 de 3
find the probability that the mean of a sample of 25 people is less than 10.
$p(\overline{x} < 10) = \square$

Explanation:

Step1: Identify parameters

Population mean $\mu=12$, standard deviation $\sigma=3.5$, sample size $n=25$, sample mean $\bar{x}=10$.

Step2: Calculate standard error

Standard error $\sigma_{\bar{x}}=\frac{\sigma}{\sqrt{n}}=\frac{3.5}{\sqrt{25}}=0.7$.

Step3: Compute z-score

$z=\frac{\bar{x}-\mu}{\sigma_{\bar{x}}}=\frac{10-12}{0.7}\approx-2.86$.

Step4: Find probability from z-table

For $z=-2.86$, the area to the left is 0.0021.

Answer:

0.0021