Question

It is noted that 8% of kaplan students are left handed if 20 (TWENTY) students are randomly selected, calculate the
1) probability that none of them are left-handed
2) probability that at most 2 are left handed,
3) standard deviation for the number of left-handed student
4)if 50 classes of 20 students are randomly selected,what is the 10 classes have no left handed students?

Can i get the Question 4?

Thank you very much

Answer 1

Answer on Question #69155 – Math – Statistics and Probability

Question

It is noted that 8% of Kaplan students are left handed if 20 (TWENTY) students are randomly selected, calculate the following:

1) probability that none of them are left-handed;

2) probability that at most 2 are left handed;

3) standard deviation for the number of left-handed student;

4) if 50 classes of 20 students are randomly selected, what is the probability that 10 classes have no left handed students?

Solution

1) $P(X = 0) = C_{20}^{0} \cdot 0.08^{0} \cdot 0.92^{20} = 0.92^{20} \approx 0.1887$.

2) $P(X \leq 2) = P(X = 0) + P(X = 1) + P(X = 2) = C_{20}^{0} \cdot 0.08^{0} \cdot 0.92^{20} + C_{20}^{1} \cdot 0.08^{1} \cdot 0.92^{19} + C_{20}^{2} \cdot 0.08^{2} \cdot 0.92^{18} = 0.7879$.

3) $\sigma = \sqrt{np(1 - p)} = \sqrt{20 \cdot 0.08 \cdot 0.92} \approx 1.2133$.

4)

$P(\text{no one in a class is left - handed}) = 0.92^{20} = 0.1887$;

$P(\text{at least one in a class is left - handed}) = 1 - 0.1887 = 0.8113$;

$P(10 \text{ classes have no left - handed students}) = C_{50}^{10} \cdot 0.1887^{10} \cdot 0.8113^{40} = 0.1370$.

Answer: 1) 0.1887; 2) 0.7879; 3) 1.2133; 4) 0.1370.

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