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.

2.

according to newton’s cannonball model, what happens if the cannonball's velocity is enough to overpower the pull of earth’s gravitystep-by-step explanation:

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