Probability/Stats Questions?

Can someone please help me solve the following questions?Scores on a test are normally distributed with a mean of 550 and a standard deviation of 80. a) If one subject is randomly selected, find the probability that the score is between 550 and 650. b) If a job requires a score in the top 80%, find the lowest acceptable score. C) If 50 subjects are randomly selected, find the probability that their mean is between 550 and 650.Thanks!!!

How's it going.a) the dif. between 650and 550 is 100. a standard dev. = 80.so we will have 34% + 13.5(.25)%= 3.375 + 34= 37.375%answer to a is 37.375%b)idkc)37.375%*50= 18.675=19 people

a) To find the probability of a variable, X, between two limits, a and b when the variable is normally distributed:P(a < X < b) = Φ[(b-µ)/σ] - Φ[(a-µ)/σ] where the values within the square brackets are standard normal z-values. Phi (Φ) is and operator that means "find the probability associated with the Z-values in the square brackets". So evaluating:P(550 < X < 650) = Φ[(650-550)/80] - Φ[(550-550)/80] P(550 < X < 650) = Φ[(650-550)/80] = Φ[1.25] - Φ[0] = 0.8944 - 0.50 = 0.3944b) You want to eliminate the bottom 20%. So the Z-value associated with the BOTTOM 20% is -0.84, and the limit for the bottom 20% is found by:-0.84 = (x - 550)/80; solving for x = 482.8. If an integer is required, then the lowest acceptable score would be 483.c) Find the probability that the sample mean is less than 650:Z = (650-550)/(80/√50) = 100/35.78) = 2.79Then Φ[2.79] - Φ[0] = 0.9974 -0.50 = 0.4974