Answer :
Answer:
0.15% of the apples have diameters that are no more than 6.18cm.
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
Approximately 68% of the measures are within 1 standard deviation of the mean.
Approximately 95% of the measures are within 2 standard deviations of the mean.
Approximately 99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 7.23, standard deviation = 0.35.
What percentage of the apples have diameters that are no more than 6.18cm?
6.18 = 7.23 - 3*0.35
So 6.18cm is three standard deviations below the mean.
99.7% of the measures are within 3 standard deviations of the mean. The normal distribution is symmetric, which means that (100-99.7)/2 = 0.15% is 3 standard deviations or more below the mean, and 0.15% is 3 standard deviations or more above the mean.
Thus, 0.15% of the apples have diameters that are no more than 6.18cm.