Question

Using the example above as a guide, fill in the missing information. Enter percentage answers to the nearest tenth.

Answer 1

Solution: We know that height of trees follows a normal distribution with mean height $\mu=60$ inches and standard deviation $\sigma =12$ inches

Now let's fill the missing values as per the normal distribution and the given information.

$a0=34.1\% of 500 = 0.341 \times 500$

           $=170.5 \approx 171$

Now, let's find the value of a1. Since the height follows normal distribution with mean 60 and standard deviation = 12. Therefore, we have:

$a1=\mu+\sigma = 60+12=72$

To find the value of a2, we need to use the empirical rule of normal distribution. According to empirical rule, the area between Mean and 1 standard deviation above mean is 34.1%. Therefore, the value of a2 is:

$a2=34.1\%$

a3 denotes the area between +1 and +2 (72 to 84 inches). According to empirical rule of normal distribution, the area between one standard deviation above mean and two standard deviation mean is 13.6%.

$\therefore a3=13.6\%$

And $a4=13.6\% of 500=0.136 \times 500=68$

Therefore, the complete table is attached here.

Answer 2

Answer:

72

34

13.6

171

68