Question

2 Questions

Use the empirical rule to estimate!
The data describing the hourly output of a production line are normally distributed,
with a mean of 35 units and a standard deviation of 3 units.

What percentage of the data falls
between 29 and 41 units?

Answer choices:
50%
68%
95%
99.7%

my second question is

What percentage of the data is
less than 32 units?

Answer choices:
15.85%
16%
84%
84.15%

Answer 1

1) 95%

2) 16%

Explanation:

29 is 2 standard deviations below the mean 35, and 41 is 2 standard deviations above 35. By the Empirical Rule, 95% of the data is covered.

Since 32 is 1 standard deviation below 35, which is 34% by the Empirical Rule, then the percentage of data that is less than 32 units would be 50%-34% = 16%