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 that 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. Compute P(X = 7). Round your answer to four decimal places. Compute P(X ≥ 3). Round your answer to four decimal places. Compute P(2 < X < 7). Round your answer to four decimal places. Compute σX, the standard deviation of X. Round your answer to four decimal places.

(a) The value of P (X = 7) is 0.1377.

(b) The value of P (X ≥ 3) is 0.9380.

(c) The value of P (2 < X < 7) is 0.5443.

(d) The standard deviation of X is 2.4495

Step-by-step explanation:

Let X = the number of tracks counted in 1 cm² of surface area.

It is provided that the average number of tracks is 6 per cm².

The random variable .

The probability function of a Poisson distribution is:

(a)

Compute the value of P (X = 7) as follows:

Thus, the value of P (X = 7) is 0.1377.

(b)

Compute the value of P (X ≥ 3) as follows:

P (X ≥ 3) = 1 - P (X < 3)

              = 1 - P (X = 0) - P (X = 1) - P (X = 2)

Thus, the value of P (X ≥ 3) is 0.9380.

(c)

Compute the value of P (2 < X < 7) as follows:

P (2 < X < 7) = P (X = 3) + P (X = 4) + P (X = 5) + P (X = 6)

Thus, the value of P (2 < X < 7) is 0.5443.

(d)

The standard deviation of a Poisson distribution is:

Compute the value of standard deviation of X as follows:

Thus, the standard deviation of X is 2.4495

y do u put "subscirbe to ence" on a app for ppl who need with their work?

option a is correct.

step-by-step explanation:

scale factor: it is used to find proportional measurements.

proportions means having the same ratio.

scale factor is the ratio of the model measurement to the actual measurement in a simplest form.

or we can say that the ratio of any two corresponding lengths in two similar geometric figures

if the scale factor is more than 1, then it is an enlargement,

if the scale factor less than 1, then it is a reduction.

given the two geometric figure:

by definition of proportions, we have