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

The required answer is shown below:

Step-by-step explanation:

Consider the provided information.

The formula for calculating poisson probability mass function:

Where λ is average number of events, the value of e = 2.718..

K can take the values 0,1,2...

Part (a)Find P(X = 7).

A certain mineral specimen is of such an age that there should be an average of 6 tracks per cm² of surface area.

Use the above formula and substitute x=7 and λ=6

Hence, P(X = 7) = 0.1377

Part (b)Find P(X ≥ 3).

This can be calculated as:

Hence, P(X ≥ 3) = 0.9380

Part (c)Find P(2 < X < 7).

The sum can be calculated as:

Hence, P(2 < X < 7)= 0.5443

Part (d)Find μX.

If λ is average number of successes or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to λ.

Part (e)Find σX

If λ is average number of successes or region in the Poisson distribution, then the mean and the variance of the Poisson distribution are both equal to λ.

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