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

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

no i do not : ( what is it?