Question

The time it takes Jessica to bicycle to school is normally distributed with mean 15 minutes and variance 4. Jessica has to be at school at 8:00 am. Suppose you saw her at class, and she said it took her 23 minutes to get to school that day. Which of the following is a reasonable inference or conclusion?a. Twenty-three minutes to school is not an unusually long commute time.b. A commuting time of 23 minutes is highly unusual or atypical.c. The distribution of commute times MAY NOT be normal with mean 15 minutes and standard deviation 2 minutes.d. Both (b) and (c) are feasible conclusions.e. Both (a) and (c) are feasible conclusions.

Answer 1

d. Both (b) and (c) are feasible conclusions

Explanation:

Given that the time it takes Jessica to bicycle to school is normally distributed with mean 15 minutes and variance 4.

i.e. X the time it takes for Jessica to reach school is N(15,2)

One day Jessica said it took 23 minutes to get to school

i.e. 4 std deviations above the mean time it took

the prob for this is almost 0 which is very unusual.

Either the distribution is not symmetric as mentioned normal or the time is unusual

Hence correct option woul dbe

b. A commuting time of 23 minutes is highly unusual or atypical. and

c. The distribution of commute times MAY NOT be normal with mean 15 minutes and standard deviation 2 minutes

So both b and c are feasible conclusions