Durva sikligar 4501574 test 2

Therefore, the mean is 20 and the standard deviation is 4 8) To determine the expected number of children in a randomly selected Canadian household, we use the formula for calculating the expected value (mean) of a discrete probability distribution: E ( X )=∑ x ⋅ P ( x )Given the probability distribution table: =1,2,3,4,5 x =1,2,3,4,5 =0.25,0.42,0.17,0.15,0.01 P ( x )=0.25,0.42,0.17,0.15,0.01 Calculate the expected number of children: =(1×0.25)+(2×0.42)+(3×0.17)+(4×0.15)+(5×0.01) E ( X )=(1×0.25)+(2×0.42)+(3× 0.17)+(4×0.15)+(5×0.01) =0.25+0.84+0.51+0.60+0.05 E ( X )=0.25+0.84+0.51+0.60+0.05 2.25 E ( X )=2.25Therefore, the expected number of children in a randomly selected Canadian household is 2.25 9) To find the probability of selecting 10 production employees at random on a hot summer day and finding that none of them are absent, we can use the binomial probability formula: P ( X = k )=( kn )× pk ×(1− p ) n − k Given:  Absenteeism rate (p) = 5% or 0.05  Number of trials (n) = 10  Finding none absent (k = 0) Substitute the values into the formula: (100)×0.050×(1−0.05)10−0 P ( X =0)=(010)×0.050×(1−0.05)10−0 1×1×0.9510 P ( X =0)=1×1×0.9510 0.5987 P ( X =0)≈0.5987Therefore, the probability of selecting 10 production employees at random and finding that none of them are absent is approximately 0.599 10) To calculate the probability that exactly 8 out of 20 high school graduates selected at random will go to college, we can use the binomial probability formula: P ( X = k )=( kn )× pk ×(1− p ) n − k Given:  Probability of a high school graduate going to college (p) = 30% or 0.30  Number of trials (n) = 20  Number of successes (k) = 8