Question

100 POINTS! ANSWER NOW! I'm really slow so please explain this as thoroughly as possible.

Answer 1

Step-by-step explanation:

a) The graph of a normal curve with a mean of 64" and a standard deviation of 3.5" is a bell-shaped curve with its

maximum value at x = 64.

Important points:

mean - 3 deviations: 64 - 3(3.5) = 64 - 10.5 = 53.5

mean - 2 deviations: 64 - 2(3.5) = 64 - 7 = 57

mean - 1 deviation: 64 - 3.5 = 60.5

mean: = 64

mean + 1 deviation: 64 + 3.5 = 67.5

mean + 2 deviations: 64 + 2(3.5) = 64 + 7 = 71

mean + 3 deviations: 64 + 3(3.5) = 64 + 10.5 = 74.5

b) If there are 3000 plants, approximately how many will be taller than 71"?

71" is 2 standard deviations above the mean. The region between two standard deviations below the mean and two standard deviations holds approximately 95% of the plants.

Therefore there will be approximately 5% of the plants divided equally between being taller than two standard

deviations above the mean and being shorter than two standard deviations below the mean. Thus, there will be

approximately 2.5% of the plants taller than 71": 0.025 x 3000 = 75 plants.

or

the z-score for 71

= (71-64)/35 = 2

going to your tables, or some other suitable source for standard deviation, we find

P(z < 2) = .9772

P(z > 2) = .0228

.0228(3000) = 68.4

or appr 68 plants