Question: Let x be a random variable that represents the length of time it takes a student to complete Dr. Tracy Wang’s homework. From long experience, it is known that x has a normal distribution with mean \[\mu =3.6\] hours and standard deviation \[\sigma =0.5\] hour.

Find the following probabilities.

1. \[P(x\ge 4.6)\]
2. \[P(x\le 4.6)\]
3. \[P(0\le x\le 4.6)\]
4. \[P(2.5\le x\le 4.5)\]

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