Let Z be a standard normal variable. Find the following probabilities: P (Z < 2.96) = P (Z > - 0.23)

Let x be a random variable that has a normal distribution with a mean of 40 and a standard deviation of 5. After converting the following x-values to z-values, find the following probabilities: P(x < 49)     P(x > 55)

Storm damage can occur to homes in any given year, with the amount of damage varying randomly from year to year. Let X represent the dollar value of storm damage in a given year. It is known that in 95% of the years, X = $0, while in 5% of the years, X = $20,000. What is the expected value and standard deviation of the damage in any given year?

Supposed Y follow a binomial distribution with n = 15 and p = 0.4. a.) Find the exact probabilities of Y < 8 and Y = 8 (from the included tables). b.) Compare these to the corresponding values found by using the normal approximation (from the included tables).

Use the z formula  and the normal table( z distribution) to solve the following problems.  the time it takes a person to lose weight following a healthy diet with regular exercise may be looked upon as a random variable having a normal distribution with mean μ = 18.4 lbs per month and standard deviation σ = 5.8 lbs per month.  Find the probabilities that during a period of healthy dieting and exercising a person's weight will be reduced by at least 20 lbs per month,between 5 and 15 lbs per month,at most 30 lbs per month and between 15 and 25 lbs per month?

Assume that daily evaporation rates (E) have a uniform distribution with a = 0 and b = 0.35 inches/day. Determine the following probabilities:Pr (E ≥0.1) Pr (E ≤ 0.22) Pr (E = 0.2) Pr (0.05 ≤ E ≤ 0.15

I have to find the value of the standard normal random variable. P (Z <= Zo) = .7054

Let Z be a standard normal random variable. Calculate the following probabilities and round your response to at least 3 decimal places. P(Z is less than or equal to -2.12)=        P(Z>-0.71)=         P(0.92<Z<2.09)=