4. geologists estimate the time since the most recent cooling of a mineral by counting the number of uranium fission tracks on the surface of the mineral. a certain mineral specimen is of such an age that there should be an average of 6 tracks per cm2 of surface area. assume the number of tracks in an area follows a poisson distribution. let x represent the number of tracks counted in 1 cm2 of surface area.

a)find p(x = 7).

b)find p(x ≥ 3).

c)find p(2 < x < 7).

d)find μx.

e)find σx

In this case we use the Poisson distribution because we are talking about the occurrence of an event (number of tracks) over a specified interval (in this case an area interval).

The probability of the event occurring x times over an interval is:

P(x) = nˣ × e⁻ⁿ ÷ x!

where n is the mean.

a) P(7) = 6⁷ × e⁻⁶ ÷ 7! = 0.1376

b) P(x ≥ 3) = 1 - P(x < 3) = 1 - P(2) - P(1) - P(0)

P(2) = 6² × e⁻⁶ ÷ 2! = 0.0446

P(1) = 6¹ × e⁻⁶ ÷ 1! = 0.0149

P(0) = 6⁰ × e⁻⁶ ÷ 0! = 0.0025

P(x ≥ 3) = 0.9380

c) P(2 < x < 7) = P(3) + P(4) + P(5) + P(6) = 0.0892 + 0.1339 + 0.1606 + 0.1606 = 0.5443

d) The mean is going to be 6.

e) The standard deviation is √n = √6 = 2.4

c.   x=2.4cm

step-by-step explanation:

similar triangles are triangles which have the same shape but not the same size. this means their angle measures are equal but their side lengths are not instead they are proportional. to solve, we will set up a proportion and solve.

a proportion is two equal ratios set equal to each other. we form the ratios by finding corresponding sides (sides which match to each other on both triangles by their position). out ratios will be one side of the small triangle over the corresponding side on the big triangle as shown below:

.

to solve the proportion, we'll cross multiply by multiplying numerator with denominator across the equal sign.