Question

The Learning target is I can find percentages and values using the 68-95-99.7 rule, z-scores, and the standard normal distribution. Draw a normal curve of this situation and label three standard deviations in either direction. Please help only answer if you can help or know the answer please appreciate it

Answer 1

According to the 68-95-99.7 rule,

68% of the outcome would lie within 1 standard deviation from the mean

95% of the outcome would lie within 2 standard deviations from the mean

99.7% of the outcome would lie within 3 standard deviation from the mean

Looking at the given scenario,

mean weight = 20

standard deviation = 6

Thus,

for 68%, it would lie within 20 +/ 6. This is within 14 and 26

for 95%, it would lie within 20 +/ 2 * 6. This is within 8 and 32

for 95%, it would lie within 20 +/ 3 * 6. This is within 2 and 38

The picture of the curve is shown below

1) We would apply the formula for determining z score which is expressed as

z = (x - mean)/ standard deviation

From the information given, x = 15, mean = 20, standard deviation = 6

z = (15 - 20)/6 = - 0.83

We would find the probability value corresponding z score from the normal distribution table. It is 0.203

Converting to percentage, it becomes 0.203 x 100 = 20.3%

Thus, 20.3% of fishes on this lake would weigh less than 15 pounds