Let \[ f(x)=\left\{\begin{array}{ll}0.048 x(5-x) & 0 \leq x \leq 5 \\ 0 & \text { otherwise }\end{array}\right. \] (a) Verify that \( f \) is a probability density function. (b) Find \( P(X \geq 4) \).

There is a 0.99962 probability that a randomly selected 23 -year-old female lives through the year. An insurance company wants to offer her a one-year policy with a death benefit of \( \$ 1,000,000 \). How much should the company charge for this policy if it wants an expected return of \( \$ 600 \) from all similar policies? The company should charge \( \$ \square \). (Round to the nearest dollar.)

A die is rolled. Find the probability of the given event. (a) The number showing is a 5 ; The probability is: (b) The number showing is an even number; The probability is : (c) The number showing is greater than 2 ; The probability is :

A poll showed that \( 50.8 \% \) of Americans say they believe that statistics teachers know the true meaning of life. What is the probability of randomly selecting someone who does not believe that statistics teachers know the true meaning of life. Report the answer as a percent rounded to one decimal place accuracy. You need not enter the "\%" symbol.

A card is drawn randomly from a standard 52-card deck. Find the probability of the given event. (a) The card drawn is 5 The probability is : \( \frac{1}{53} \) (b) The card drawn is a face card (Jack, Queen, or King) The probability is : (c) The card drawn is not a face card. The probability is:

A card is drawn randomly from a standard 52 -card deck. Find the probability of the given event. (a) The card drawn is 5 The probability is : (b) The card drawn is a face card (Jack, Queen, or King) The probability is: (c) The card drawn is not a face card.