1 point)
Suppose the flight time between Montreal and Toronto follows a normal distribution with an average of 60 minutes and a standard deviation of 4
minutes. Mary is taking a flight tomorrow morning between these two cities. What is the probability that Mary's flight time will be between 49
minutes and 63 minutes? □

Question

1 point) 
Suppose the flight time between Montreal and Toronto follows a normal distribution with an average of 60 minutes and a standard deviation of 4
minutes. Mary is taking a flight tomorrow morning between these two cities. What is the probability that Mary's flight time will be between 49
minutes and 63 minutes? □

GauthUser2678 · Accepted Answer

The probability that the flight time will be between 49 and 63 minutes is: 0.77039. Explanation 
The problem could be solved through the standardization or "z -scoring" of the normal distribution: 
For any random variable following a normal distribution, the standardized value (z-score) is calculated by taking the 
difference between the value of interest and the mean (which is 60 minutes in this case), and subsequently dividing 
by the standard deviation (which is 4 minutes in this case). 
Once the z-scores are known, we can calculate the probabilities using a standard normal distribution table. 
So, let's find the z-score for 49 minutes and 63 minutes : 
Z-score 1=(49-60)/4=-2.75
Z-score 2=(63-60)/4=0.75
Now we find the area under the curve for these z-scores in a standard normal distribution table which provides the 
probability of the z-score values. The values for these particular Z scores, derived from a z -table or a standard normal 
distribution calculator, are as follows:
Z-table(Z-scorel=-2.75)=0.00298
Z-table(Z-score2=0.75)=0.77337
To determine the probability that the flight time will be between 49 and 63 minutes, we subtract the probability of Z - 
score 1 from the probability of Z-score 2. 
Probabilit y=Z-table(Z-score2)-Z-table(Z-score1)=0.77337-0.00298=0.77039
Therefore, the probability that the flight time will be between 49 and 63 minutes is: 0.77039

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