A boardwalk is to be erected along an ocean beach. The specifications for the boardwalk require a width of at least 155 cm., but the pre-cut pieces of lumber supplied for the boardwalk are uniformly distributed in length between 148 cm. and 164 cm.

a)

b)

c)

d)

e) Step-by-step explanation:

Assuming the following questions:

a. The distribution is X Use whole numbers.

Let X the random variable that represent the "lenght of pieces" used for the construction. We know that X follows an uniform distribution given by:

b. The average length of the pieces of lumber is cm. Use whole numbers.

For this case the expected value for the distribution is given by:

c. Find the standard deviation.

First we need to calculate the variance given by:

d. What's the probability that a randomly chosen piece of lumbar will be less than the required lenght?

For this case we can use the density function for X given by:

And the cumulative distribution function would be given by:

We want to find this probability:

e. Find the probability that a randomly chosen piece of lumber will be between 155 and 160 cm long?

For this case we want this probability:

And we can use the cdf function and we have:

answer: 180

step-by-step explanation:

12-2=10

20-2=18

10x18=180

d

step-by-step explanation: