Mathematics, 05.05.2020 22:20 jby

When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 972 comma 737 radioactive atoms, so 27 comma 263 atoms decayed during 365 days.

a. Find the mean number of radioactive atoms that decayed in a day.

b. Find the probability that on a given day, 51 radioactive atoms decayed.

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Answer from: nina4552

a) 74.69

b) 0.08% probability that on a given day, 51 radioactive atoms decayed.

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

In which

x is the number of sucesses

e = 2.71828 is the Euler number

$\mu$ is the mean in the given time interval.

a. Find the mean number of radioactive atoms that decayed in a day.

27,263 atoms in 365 days. The mean is

$\mu = \frac{27263}{365} = 74.69$

b. Find the probability that on a given day, 51 radioactive atoms decayed.

This is P(X = 51).

$P(X = x) = \frac{e^{-\mu}*\mu^{x}}{(x)!}$

$P(X = x) = \frac{e^{-74.69}*(74.69)^{51}}{(51)!} = 0.0008$

0.08% probability that on a given day, 51 radioactive atoms decayed.

Answer from: Quest

$79500

step-by-step explanation:

75000÷100=750750×106=79500

Answer from: Quest

step-by-step explanation:

i found the life tables for the year 2012.

life table of males at age 30. probability of dying between ages x and x+1

total population:

29–30 . . . . . . . . . . . . 0.001030

30–31 . . . . . . . . . . . . 0.001061

males:

29–30 . . . . . . . . . . . . 0.001420

30–31 . . . . . . . . . . . . 0.001448

white population

29–30 . . . . . . . . . . . . 0.001005

30–31 . . . . . . . . . . . . 0.001037

white males

29–30 . . . . . . . . . . . . 0.001372

30–31 . . . . . . . . . . . . 0.001399

non hispanic white population

29–30 . . . . . . . . . . . . 0.001083

30–31 . . . . . . . . . . . . 0.001116

non hispanic white males

29–30 . . . . . . . . . . . . 0.001477

30–31 . . . . . . . . . . . . 0.001503

jacob, non hispanic white male. 30 years old.

probability that jacob lives to be 30 years old.

since the given probabilities are probabilities of dying, i think we simply subtract it from 1 to get the probability of living. we will use the probability of non hispanic white male.

probability of living to be 30 y.o.

29 - 30 : 1 - 0.001477 = 0.998523

30 - 31 : 1 - 0.001503 = 0.998497

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When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioacti...

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