An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

The possible values of the random variable X are the crew sizes: 4, 6, 7, 8, 9, and 10.
The event of a shuttle mission with a crew size of 9 is represented as P ( X = 9 ) .
The probability P ( X = 6 ) is calculated as 143 4 ​ ≈ 0.028 , meaning 2.8% of shuttle crews consist of exactly 6 people.
The probability distribution of X is: P ( X = 4 ) ≈ 0.035 , P ( X = 6 ) ≈ 0.028 , P ( X = 7 ) ≈ 0.217 , P ( X = 8 ) ≈ 0.182 , P ( X = 9 ) ≈ 0.524 , P ( X = 10 ) ≈ 0.014 .

Explanation

Identify possible values of X a. The possible values of the random variable X are the crew sizes listed in the table. These are the numbers of crew members that were observed on the space shuttle missions.

List possible values The possible values of X are 4, 6, 7, 8, 9, and 10.

Represent event with notation b. The event that the shuttle mission obtained has a crew size of 9 is represented in random-variable notation as P ( X = 9 ) . This notation means 'the probability that the random variable X is equal to 9'.

Select correct choice The correct choice is A. P ( X = 9 )

Calculate P(X=6) c. To find P ( X = 6 ) , we need to divide the frequency of shuttle missions with a crew size of 6 by the total number of shuttle missions. First, we calculate the total number of missions.

Calculate total missions The total number of shuttle missions is 5 + 4 + 31 + 26 + 75 + 2 = 143 .

Calculate probability Now, we calculate P ( X = 6 ) by dividing the frequency of crew size 6 (which is 4) by the total number of missions (143): P ( X = 6 ) = 143 4 ​ ≈ 0.028 .

Convert to percentage To interpret this as a percentage, we multiply by 100: 0.028 × 100 = 2.8% .

Interpret as percentage This means that approximately 2.8% of shuttle crews consist of exactly 6 people.

Select correct choice The correct choice is A. 2.8% of shuttle crews consist of exactly 6 people.

Obtain probability distribution d. To obtain the probability distribution of X , we need to calculate the probability for each possible value of X . We do this by dividing the frequency of each crew size by the total number of missions (143).

Calculate probabilities P ( X = 4 ) = 143 5 ​ ≈ 0.035
P ( X = 6 ) = 143 4 ​ ≈ 0.028
P ( X = 7 ) = 143 31 ​ ≈ 0.217
P ( X = 8 ) = 143 26 ​ ≈ 0.182
P ( X = 9 ) = 143 75 ​ ≈ 0.524
P ( X = 10 ) = 143 2 ​ ≈ 0.014

Present probability distribution The probability distribution of X is as follows:


Examples
Understanding the distribution of crew sizes on space shuttle missions can help in planning future missions. For example, if a new mission requires a specific skill set that typically requires a larger crew, the probability distribution can show how often missions with larger crews have occurred in the past. This can inform decisions about resource allocation and crew selection. Also, it can be used to estimate costs associated with different crew sizes, as larger crews may require more resources and support. For instance, knowing that missions with 9 crew members occurred most frequently (52.4%) can help in budgeting and logistical planning for future missions.

Answered by GinnyAnswer | 2025-07-07

A current of 15.0 A flowing for 30 seconds results in a total charge of 450 C . Using the charge of a single electron, approximately 2.81 × 1 0 21 electrons flow through the device during this time. This demonstrates the relationship between current, time, and charge in an electrical circuit.
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Answered by Anonymous | 2025-07-28