Question

The annual increase in height of cedar trees is believed to be distributed uniformly between five and ten inches. Find the probability that a randomly selected cedar tree will grow less than 8 inches in a given year. Round your answer to four decimal places, if necessary.

Answer 1

Answer:

1(1/7) or 0.1428

Step-by-step explanation:

To find the probability of a randomly selected ceder tree that will grow less than 8 inches in a given year is,

lets Recall that Area= Width x Height

The number 12 is  declared as a given year (1 year)

Therefore

The height= 1/12-5= 1/7

The width= 6-5=1

For area=  1(1/7)

1(1/7)=0.1428

Answer 2

Answer: 0.6000

Step-by-step explanation:

Given : The annual increase in height of cedar trees is believed to be distributed uniformly between 5 and 10 inches.

Then the probability density function:-

$f(x)=\dfrac{1}{10-5}=\dfrac{1}{5}$

Then , the  probability that a randomly selected cedar tree will grow less than 8 inches in a given year will be :-

$P(x\leq8)=\int^8_5f(x)\ dx\\\\=\int^8_5(\dfrac{1}{5})\ dx\\\\=\dfrac{1}{5}[x]^8_5\\\\=\dfrac{1}{5}\times(8-5)=\dfrac{3}{5}=0.6000$

Hence, the probability that a randomly selected cedar tree will grow less than 8 inches in a given year =0.6000