Provide an appropriate response 1) 15% percent of the population is left-handed.

Question

Provide an appropriate response 1) 15% percent of the population is left-handed. A class of 5600 students is selected. Convert the binomia 31) to a normal probability by using the correction for continuity probability P(x 2) The success rate in a statistics class is 80%. In a class of 90 students, find the probability that exactly five students will pass. Use the normal distribution to approximatethe binomial distribution First check if the approximation to a normal distribution is possible. 3) Same question: The success rate in a statistics d assi s 80%. In a class of 90students, find the probabil ity that exactly five students will pass. Usethe cal culation for binomial probabilities

Explanation / Answer

1) Mean = n*p = 5600*0.15 = 840, SD = sqrt(n*p*q) = sqrt(5600*0.15*0.85) = 26.72078

Formula: Z = (X - mean)/SD

P(X >= 31) = P(X > 30.5) = P(Z > (30.5 - 840)/26.72078) = P(Z > -30.29)

2) For approximation, np >=5 and n(1-p) >= 5
90*0.2 = 18, approximation is possible

Mean = 90*0.8 = 72, SD = sqrt(90*0.8*0.2) = 3.7947
P(X = 5) = P(<=5) - P(X <=4) = P(X < 5.5) - P(X < 4.5) = P(Z < (5.5-72)/3.7947) - P(Z < (4.5-72)/3.7947) = 0 for such low z values

3) P(X = 5) = 90C5 * 0.85 * 0.285 = 5.57 * 10-53

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