Questions from Calculus

Q: Show that the function f (x) = e-x2

Show that the function f (x) = e-x2/2 has inflection points at x = ± 1.

Q: Show that the function f (x) = e-(1

Show that the function f (x) = e-(1/2)[(x-µ)/σ]2 has inflection points at x = m ± s.

Q: Let Z be a standard normal random variable. Calculate (

Let Z be a standard normal random variable. Calculate (a) Pr (-1.3 ≤ Z ≤ 0) (b) Pr (.25 ≤ Z) (c) Pr (-1 ≤ Z ≤ 2.5) (d) Pr (Z ≤ 2)

Q: Calculate the area under the standard normal curve for values of z

Calculate the area under the standard normal curve for values of z (a) between .5 and 1.5, (b) between -.75 and .75, (c) to the left of -.3, (d) to the right of -1.

Q: The gestation period (length of pregnancy) of a certain species

The gestation period (length of pregnancy) of a certain species is approximately normally distributed with a mean of 6 months and standard deviation of 12 month. (a) Find the percentage of births tha...

Q: The condenser motor in an air conditioner costs $300 to replace

The condenser motor in an air conditioner costs $300 to replace, but a home air-conditioning service will guarantee to replace it free when it burns out if you will pay an annual insurance premium of...

Q: Suppose that the life span of a certain automobile tire is normally

Suppose that the life span of a certain automobile tire is normally distributed, with µ = 25,000 miles and σ = 2000 miles. (a) Find the probability that a tire will last between 28,000 and 30,000 mil...

Q: If the amount of milk in a gallon container is a normal

If the amount of milk in a gallon container is a normal random variable, with µ = 128.2 ounces and σ = .2 ounce, find the probability that a random container of milk contains less than 128 ounces.

Q: The amount of weight required to break a certain brand of twine

The amount of weight required to break a certain brand of twine has a normal density function, with µ = 43 kilograms and σ = 1.5 kilograms. Find the probability that the breaking weight of a piece of...

Q: A student with an eight o’clock class at the University of Maryland

A student with an eight o’clock class at the University of Maryland commutes to school by car. She has discovered that along each of two possible routes her traveling time to school (including the tim...