1. If x is a normally distributed random variable with =24=24 and =5=5, then where will the density curve for x be centered, and where will its inflection points be located?

center at x =

lesser-valued inflection point at x =

greater-valued inflection point atx=

2. About ------- % of the area under the curve of the standard normal distribution is outside the interval z=[1.65,1.65] (or beyond 1.65 standard deviations of the mean).

After converting your answer to a percentage, round it to 2 places after the decimal point, if necessary.

3. For the standard normal distribution, find the value of cc such that: P(z>c)= 0.6325 c = (Round your answer to 3 places after the decimal point, if necessary.)

4. Assume thatxx is a normally distributed random variable with =12.6 and=3.1

FindP(x > -8.167)

Round your answer 4 places after the decimal point.

5. A manufacturer knows that their items have a normally distributed lifespan, with a mean of 3.5 years, and standard deviation of 0.5 years. If you randomly purchase one item, what is the probability it will last longer than 2.5 years? (Round your final answer to 3 places after the decimal point.)