1. Given the X and the probability distribution, fill in the table and calculate the variance, a standard deviation of the following the probability distribution. X P(X) X. P(X) x2. P(X) 0.28 1 .32 0.20 3 0.10 4 0.10 2. A concerned group of mothers determined the number of commercials X shown in five TV programs for children. Find the variance and standard deviation for the distribution shown. 10 12 14 P(X) 0.20 0.25 0.38 0.10 0.07 B. Solve the following problems. You may apply either of the two formulas. 1. A basketball player shoots three free throws. The number of baskets successfully made is the random variable X. Given the value of u = 1.8, compute for the variance and standard deviation of the distribution. Value of X 1 3 Probability 0.064 0.288 0.432 0.216 2. A radio station has six telephone lines. If the host is unable to talk or is talking to another person, the other callers are placed on hold. When all telephone numbers are in occupied, you're getting an all circuits busy. The probability that 0, 1, 2, 3 or 4 people will get through is 0.22, 0.10, 0.21, 0.23, and 0.24, respectively. Give the variance and the standard deviation of the distribution.