Question

The time for a certain female student to commute to SCSU is Normally Distributed with mean 32.5 minutes and standard deviation of 6.5 minutes.

1. Find the probability her commuting time is more than 40 minutes.
2. Find the probability her commuting time is less than 43 minutes.
3. Find the value t such that 10% of her commuting times are greater than t.
4. Between which two values will the middle 70% of her commuting times fall?
5. Find the probability her commuting time is between 31.5 and 42.5 minutes.

Answer 1

Here distribution is normal with mean=32.5 and standard deviation=6.5

As distribution is normal we can convert x to z

Here we need to find t, such that

Using z table we get

So

Hene

Now we need to find x1 and x2 such that

Using z table we get

So

Hence

Similarly

Now we need to find