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Sever21 [200]
3 years ago
8

Normal Distribution. Cherry trees in a certain orchard have heights that are normally distributed with mu = 112 inches and sigma

= 14 inches. What is the probability that a randomly chosen tree is greater than 140 inches? For this problem we want just the answer. Please give up to 4 significant decimal places, and use the proper rules of rounding.
Mathematics
1 answer:
Lubov Fominskaja [6]3 years ago
5 0

Answer:

The probability that a randomly chosen tree is greater than 140 inches is 0.0228.

Step-by-step explanation:

Given : Cherry trees in a certain orchard have heights that are normally distributed with \mu = 112 inches and \sigma = 14 inches.

To find : What is the probability that a randomly chosen tree is greater than 140 inches?

Solution :

Mean - \mu = 112 inches

Standard deviation - \sigma = 14 inches

The z-score formula is given by, Z=\frac{x-\mu}{\sigma}

Now,

P(X>140)=P(\frac{x-\mu}{\sigma}>\frac{140-\mu}{\sigma})

P(X>140)=P(Z>\frac{140-112}{14})

P(X>140)=P(Z>\frac{28}{14})

P(X>140)=P(Z>2)

P(X>140)=1-P(Z

The Z-score value we get is from the Z-table,

P(X>140)=1-0.9772

P(X>140)=0.0228

Therefore, the probability that a randomly chosen tree is greater than 140 inches is 0.0228.

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