Answer:
84% of the apples have diameters that are greater than 7.07cm.
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.
Also, since the normal distribution is symmetric:
50% of measures are above the mean and 50% are below.
Of those 68% within 1 standard deviation of the mean, 34% are between one standard deviation below the mean and the mean, and 34% are between the mean and one standard deviation above the mean.
Of those 95% within 2 standard deviation of the mean, 47.5% are between two standard deviations below the mean and the mean, and 47.5% are between the mean and two standard deviations above the mean.
Of those 99.7% within 3 standard deviation of the mean, 49.85% are between 3 standard deviations below the mean and the mean, and 49.85% are between the mean and 3 standard deviations above the mean.
In this problem, we have that:
Mean = 7.46cm
Standard deviation = 0.39 cm
Using the empirical rule, what percentage of the apples have diameters that are greater than 7.07cm?
7.07 is one standard deviation below the mean.
50% of apples have diameters above the mean, that is, 50% of the apples have diameters above 7.46cm.
34% have diameters between one standard deviation below the mean and the mean, that is, between 7.07cm and 7.46cm.
So 84% of the apples have diameters that are greater than 7.07cm.
