Probabilities With The Binomial Distribution

Calculate the mean, variance, and standard deviation for this distribution: The mean is 17%, or 0.17; the variance is 0.1509 and the standard deviation is 0.387567431 . Calculate the probability that at least 3 people in the sample checked the weather that day: The probability that at least 3 people in the sample checked the weather that day is 0.0045 (or 4.5%). According to a recent infographic (NAMI: National Alliance on Mental Illness, n.d.), \"1 in 20 U.S. adults experience serious mental illness\" in the United States If a random sample of 20 students is selected from a large school district, construct a table of the binomial probability distribution for this case: Number of Students Diagnosed with Serious Mental Illness | Probability 0 | (.95)^20 = .621341841                   1        20C1* (1-.95)^1*. 95^19= .235357068                     2                 20C2*(1-.95)^2*. 95^18= .096372793                                          3                        20C3*(1-.95) ^3 *. 95 ^17= .029078833                                        4                           20C4 * (1-.95) ^4 * 95 ^16= .007391177 5    20C5 * (1-.95 )5 * 95 ^15 = .001553469 View this information using a histogram: Calculate the mean, variance, and standard deviation for this distribution: The mean number of students out of twenty who will be diagnosed with seriousmental illness is 1;the varianceis0.3250andthestandarddeviationis057217967 If 3 ofthestudentswerediagnosedwithseriousmentailnesswouldthisbesignalabouttheschooldistricthavingproblemwithmentalhealthamongthestudentsbeing abovenationalscore? Yes,itwouldbeasignalthattheschooldistrictmayhaveaproblemwithhighratesofmentalillnesscomparedtonation

Sample Solution

Construct a table of the binomial probability distribution for this case: Number of People Checking Weather | 0 | 1 | 2 | 3 | 4 | 5 Probability | 0.83| 0.17|0.028|0.0045|0.0006|0.00003 View this information using a histogram: