Pepper plants watered lightly every day for a month show an average growth of 27 centimeters with a standard deviation of 8.3 centimeters, while pepper plants watered heavily once a week for a month show an average growth of 29 centimeters with a standard deviation of 7.9 centimeters. in a simple random sample of 60 plants, half of which are given each of the watering treatments, what is the probability that the difference in average growth between the two halves is between - 3 an + 3 centimeters?

Question

Mathematics

Kaiya Cook

22 March, 04:14

Pepper plants watered lightly every day for a month show an average growth of 27 centimeters with a standard deviation of 8.3 centimeters, while pepper plants watered heavily once a week for a month show an average growth of 29 centimeters with a standard deviation of 7.9 centimeters. in a simple random sample of 60 plants, half of which are given each of the watering treatments, what is the probability that the difference in average growth between the two halves is between - 3 an + 3 centimeters?

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Duncan Villarreal · Answer 1

The difference in the mean will be (μ1-μ2) = 27-29 = - 2

and the probability range is - 3∠x∠ 3

Working with standard deviations for the half sets 30 and 30 for the two sets;

σ = √ ((8.3²/30) - (7.9²/30)

= 2.092

Thus, (-3 - (-2)) / 2.092 ∠ x ∠ (3 - (-2)) / 2.092

= - 0.48 ∠ x ∠ 2.39

Probability = 1 - normal cdf

Normal cdf = (-5, - 0.48) ∠ x ∠ (5, 2.39)

= 0.3156 ∠ р ∠ 0.9916

Therefore, probability = 0.9916 - 0.3156 = 0.6760

Thus the probability will be equivalent to 0.6760