Respuesta :
Answer:
0.6826
Step-by-step explanation:
To solve this, we find the z scores for both sample means. We then us a z table to find the area under the curve to the left of (probability less than) each z score, and subtract them to find the area between them.
The formula we use, since we are using sample means, is
[tex]z=\frac{\bar{X}-\mu}{\sigma \div \sqrt{n}}[/tex]
Our x-bar will be 116 in the first z-score and 120 in the second; our mean, μ, is 118; our standard deviation, σ, is 6.3; and our sample size, n, is 10:
[tex]z=\frac{116-118}{6.3\div \sqrt{10}}=\frac{-2}{1.9922}\approx -1.0039\\\\z=\frac{120-118}{6.3\div \sqrt{10}}=\frac{2}{1.9922}\approx 1.0039[/tex]
Using a z table, we see that the area under the curve to the left of -1.00 is 0.1587. The area under the curve to the left of 1.00 is 0.8413. This makes the area between them
0.8413-0.1587 = 0.6826.
