Answer:
16% of the apples have diameters that are less than 6.82cm
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed(bell-shaped) 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 = 7.25cm
Standard deviation = 0.43cm
The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.
Using the empirical rule, what percentage of the apples have diameters that are less than 6.82cm?
6.82 = 7.25 - 1*0.43
So 6.82 is one standard deviation below the mean.
Of the 50% of the diameters below the mean, 68% are within 1 standard deviation of the mean.
So 100-68 = 32% are not within 1 standard deviation of the mean.
0.5*0.32 = 0.16
16% of the apples have diameters that are less than 6.82cm
