The time it take Claudia to drive to work is normally distributed with a mean of 46  2 minutes and a standard deviation of 5 minutes. What percentage of the time will it take her less than 61 minutes to drive to work?

Bam 313 week 3 assignment part 2 statisitcs

The time it takes Claudia to drive to work can be modeled using a normal distribution with a mean of 46 minutes and a standard deviation of 5 minutes. According to the empirical rule, approximately 68% of her trips will take between 41 minutes (46 – 5) and 51 minutes (46 + 5). Since Claudia’s trip will take less than 61 minutes if it is less than 51 minutes, we can assume that 68% of the time she should be able to make it to work in an hour or less.

To calculate exactly what percentage of the time she would arrive in under 61 minutes, we can use the cumulative probability function. To find this, we must first convert her desired travel time into standard units by subtracting the mean from each value and dividing by the standard deviation. The resulting z-score for 61minutes would be 1.2 (-4/5). Now using this z-score, we can plug this into a calculator that uses cumulative probabilities and get our answer: 87.03%. This means that 87.03% of the time Claudia should arrive at work in less than 61minutes  (or one hour).

By modeling Claudia’s commute times using a normal distribution with a mean of 46 mins and standard deviation of 5mins , we are able to generate useful statistics about how long on average her commutes tend to be as well as providing us with information such as what percentage of commutes will take longer than or shorter than certain amounts of time (in this case, under 60 mins). With this valuable data on hand, Claudia is now better equipped when planning her daily commute.