An unfair die looks like an ordinary six-sided die but the outcomes are not equally likely. The probability distribution of the face value, , is as follows:   1 2 3 4 5 6 Total   0.13 0.2 0.33 0.19 0.13 0.02 1 The expected value is computed, E[X]=3.05E[X]=3.05 . Compute the variance and standard deviation:   (Round the answer to 4 decimals)

Assume the random variable X is normally distributed, with mean μ = 53 and standard deviation o=9. Find the 15th percentile. The 15th percentile is (Round to two decimal places as needed.)

Consider a random variable X that follows a normal distribution with a mean (μ) of 50 and a standard deviation (σ) of 5. Calculate the probability that X is less than 40.

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?