Gravel is graded by how fine the stones are. For a particular grade of gravel, there are 26 stones with a diameter of 0.75 inches or greater per one cubic yard of gravel, on average. (a) We would like to determine the probability of finding at most two stones with a diameter of 0.75 inches or greater in one cubic foot of the same gravel. Which of the following is the correct probability statement? P(x < 2) PX S2) P(x > 2) P(X22) (b) We would like to determine the probability of finding at most two stones with a diameter of 0.75 inches or greater in one cubic foot of the same gravel. (1 cubic yard = 27 cubic feet. Round your answer to three decimal places.) 0.960 HE -0.963 27

p(x≤2)

0.926

Step-by-step explanation:

1. The probability of getting 2 stones with a diameter of 0.75 or greater can be given as

P(x≤2)

2. We have λ = 26/27

= 0.963 per cubic foot

We use the poisson distribution here;

P(x) = e^-λ(Rλ)^x/x!

P(x≤2) = p(x=0)+p(x=1)+p(x=2)

= e^-0.963 + e^-0.963(0.963) + e^-0.963(0.963)²/2!

= 0.3817+0.3675+0.1769

= 0.926

the 3rd option is right

step-by-step explanation:

answer set (b) 0.5, 3/4 80% is in order from least to greatest.  

step-by-step explanation:

in order to compare rational numbers to each other, it is much easier if they are in the same form.   typically, the best form in which to evaluate rational numbers is in decimals.   in order to convert a percent to a decimal, you would divide the given percentage by 100.   you can also accomplish the conversion by moving the decimal point over two places to the left.   for example, the decimal value of 80% is 80/100, or 0.8.   in order to convert a fraction to a decimal, you need to divide the numerator by the denominator.   for example, 3/4 is 0.75.   so, for choice (b) 0.5 3/4 (0.75), 80% (0.8) is the only choice in which the numbers are in order from least to greatest.