Answer:
95%
Step-by-step explanation:
Assuming the distribution is normally distributed with a mean of
[tex] \mu = 15.2[/tex]
and standard deviation
[tex] \sigma =0 .9[/tex]
We want to find the probability that X is between 14.3 and 16.1
[tex]P(14.3\: < \: X\:<\:16.1)[/tex]
We find z-scores to get:
[tex]P( \frac{14.3 - 15.2}{0.9} \: < \:z\:<\: \frac{16.1 - 15.2}{0.9} )[/tex]
We simplify to get:
[tex]P( - 1 \: < \:z\:<\: 1)[/tex]
According to the empirical rule, approximately 95% of the distribution falls within one standard deviation of the mean.
