Answer to Question #328696 in Statistics and Probability for Peter

Question

1.In a box, there are 4 types [Hearts, Clubs, Diamonds, Scorpions] of cards. There are 6 Hearts cards, 7 Clubs cards, 8 Diamonds cards and 5 Scorpions cards in the box. Two cards are selected randomly without replacement.

a) Find the probability that the both selected cards are Hearts.

b) Find the probability that one card is Clubs and the other card is Diamonds.

c) Find the probability that the both selected cards are from the same type.

2.In a boys’ school, there are 45 students in grade 10. The height of the students was measured. The mean height of the students was 154 cm and the standard deviation was 2 cm. Alex’s height was 163 cm. Would his height be considered an outlier, if the height of the students were normally distributed? Explain your answer.

Answer 1

$a:\\P=\frac{C_{6}^{2}}{C_{26}^{2}}=0.0461538\\b:\\P=\frac{7\cdot 8}{C_{26}^{2}}=0.172308\\c:\\P=\frac{C_{6}^{2}+C_{7}^{2}+C_{8}^{2}+C_{5}^{2}}{C_{26}^{2}}=0.227692\\2:\\Q_1=\mu +\sigma z_{0.25}=154+2\cdot \left( -0.675 \right) =152.65\\Q_3=\mu +\sigma z_{0.75}=154+2\cdot 0.675=155.35\\Upper\,\,inner\,\,fence:\\Q_3+1.5\left( Q_3-Q_1 \right) =159.4<163\\Upper\,\,outer\,\,fence:\\Q_3+3\left( Q_3-Q_1 \right) =163.45>163\\163 is\,\,mild\,\,outlier, it\,\,is\,\,close\,\,to\,\,outer\,\,fence. Hence\,\,Alex's\,\,height\,\,would\,\,be\,\,considered\,\,as\,\,outlier.$