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:

to find the unit price, we must figure out the cost of one item (in this case one dish towel).   to do this, we divide the total price ($7.92) by the number of items bought (for this problem it is 8, because there are eight dish towels in one pack).  

$7.92/8 = $0.99

therefore, the unit price, or the price of one dish towel, is $0.99.

hope this !

y-1700=200(x+4)

step-by-step explanation:

200(x+4) is 200x + 800 she is saving 200 per week x is the weeks and the -1700 is. us that’s howmuch she already had