Consumer Reports rated airlines and found that 80% of the flights involved in the study arrived on time (that is within 15 minutes of scheduled arrival time). Assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 200 flights. What is the expected number that will arrive on time? What is the deviation of this distribution
.8*200 = 160
then
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To find the expected number of flights that will arrive on time, we can multiply the on-time arrival rate by the total number of flights in the sample.
Given that the on-time arrival rate is 80%, we can calculate the expected number of flights as follows:
Expected Number of On-Time Flights = On-Time Arrival Rate * Total Number of Flights
= 0.80 * 200
= 160 flights
Therefore, we can expect 160 out of the 200 flights in the sample to arrive on time.
To find the deviation of this distribution, we need to calculate the standard deviation. The standard deviation measures how spread out the data is from the mean.
The standard deviation (σ) can be calculated using the formula:
σ = √(n * p * (1 - p))
Where:
n is the sample size (total number of flights)
p is the on-time arrival rate
Using the values provided, we can calculate the standard deviation as follows:
σ = √(200 * 0.80 * (1 - 0.80))
= √(200 * 0.80 * 0.20)
= √(32)
= 5.66
Therefore, the deviation of this distribution is approximately 5.66.