Answer:
7788 observations are expected to be below a value of 242.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 188, standard deviation = 18
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Percentage of observations below 242:
242 = 188 + 3*18
So 242 is three standard deviations above the mean
Of the measures below the mean, all are below 242.
Of the measures above the mean, 99.7% are between the mean of 188 and three standard deviations above the mean(242). So the percentage is:
[tex}P = 0.5 + 0.997*0.5 = 0.9985[/tex]
Number of observations below 242:
99.85% of 7800 observations
0.9985*7800 = 7788
7788 observations are expected to be below a value of 242.
