When studying radioactive material, a nuclear engineer found that over 365 days, 1,000,000 radioactive atoms decayed to 970,258 radioactive atoms, so 29,742 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, 50 radioactive atoms decayed.
a. The mean number of radioactive atoms that decay per day is
(Round to three decimal places as needed.)

a) The mean number of radioactive atoms that decay per day is 81.485.

b) 0% probability that on a given day, 50 radioactive atoms decayed.

Step-by-step explanation:

Poisson distribution:

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

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in the given interval.

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

29,742 atoms decayed during 365 days, which means that:

The mean number of radioactive atoms that decay per day is 81.485.

b. Find the probability that on a given day, 50 radioactive atoms decayed.

This is P(X = 50). So

0% probability that on a given day, 50 radioactive atoms decayed.

2 & 7

step-by-step explanation:

he climbs 300 ft/hr at a constant rate. the peak is at 1,500 ft.

when going up, he reaches 600 ft in 2 hours. remember, that he is going in a constant rate. divide 600 with 300:

600/300 = 2

assuming that he takes the same route back (meaning that it's a 1500 ft route back, you can solve.

note also that you are solving when he gets back to 600 ft after he reaches the peak.

first, find the amount of hours it takes to get up the peak. divide the total amount (1500), with the ft/her (300) to get the amount of hours (x):

1500/300 = x

x = 5

it takes jamie 5 hours to get up. now, he is returning down, and reaches 600 (his current destination). remember that he climbs at a constant 300 ft/hr. divide 600 with 300:

600/300 = x

x = 2

now add the two numbers together.

x = 5 + 2 = 7

jamie takes 7 hours to go up the mountain and reach his current position when descending.

(total amount/constant rate) = (time).

remember that it is a constant rate, so in total, when he gets back down the mountain, it will take the same amount of time as when he goes up. the total amount for the round trip is: 5 + 5 = 10.

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