Suppose that diameters of a new species of apple have a bell-shaped distribution with a mean of 7.13cm7.13⁢cm and a standard deviation of 0.39cm0.39⁢cm. using the empirical rule, what percentage of the apples have diameters that are less than 6.35cm6.35⁢cm? do not round your answer.

6.35 is 2 standard deviations below the mean of 7.13, so the empirical rule tells you 2.5% are in the lower tail of the distribution.

The empirical rule says 95% are within 2 standard deviations of the mean, so 5% are outside that range. Those 5% are evenly split between the upper and lower tails of the distribution, so 5%/2 = 2.5% are in the lower tail, below -2 standard deviations.

The value 6.35 is 0.78 = 2×0.39 less than the mean of 7.13.

step-by-step explanation: