The Netherlands is one of the world leaders in the production and sale of tulips. Suppose the heights of the tulips in the green house of rotterdams fantastic flora follow a continuous uniform distribution with lower bound of 7 inches and upper bound of 16 inches. You have come to the greenhouse to select a bouquet of tulips, but only tulips with a height greater than 10 inches may be selected. What is the probability that a randomly selected tulip is tall enough to pick ____

The heights of the tulips follow continuous uniform distribution with the lower bound of 7 inches and upper bound of 16 inches.

Now the height of this density function is defined as,

f(x) = 1/( b – a ) ….

Where, the height of the tulips is denoted as x.

The lower bound of this distribution is denoted as a . Here,a = 7 ...

The upper bound of this distribution is denoted as b. Here, b =16….

Then, substituting the value in the respective positions,

we have

f(x) = 1/( 16 - 7 )= 1/9 …

Thus, the height of this density function is 1 / 9 . According to the given information, if the height of the tulip is more than 10 inches, the tulip is tall enough to pick.

Now, the probability that the height of the tulips is more than 10 inches is defined as,

p(x >10) = 16 &10 f(x)dx ......

Now, substituting the value in the respective positions,

we have p(x >10)

=16 &10 (1/9) dx

= 1/9 (16 - 10)

= 0.6667 ...

Then, the probability that the height of the tulips is more than 10 inches is 0.6667 ....

This implies, the probability that a randomly selected tulip is tall enough to pick is 0.6667 ..…