Answer:
The probability that she will be able to get to bed in time is 66%
Explanation:
Hi!
The solution of this problem is given by the cumulative disrtibution of the normal distribution, we must integrate that pdf from -∞ to 4 hours, which is the time until its 10:00 pm.
Anologously we can use the Z score needed and look for tables and know the probability.
The Z score is given by:
Z = (x- m)/σ
Z = (4 -3.5)/1.2 =0.416
In the tables we find that for:
Z = 0.41 ----> P=0.65910
Z = 0.42 ----> P=0.66276
Therefore, if we consider only two significant figures we can say that:
The probability that she will be able to get to bed in time is 66%