There are 25 students in a class. The table shows the distribution of the heights of these students.
Find the interval that contains the median height.[1]
Calculate an estimate of the mean height.[1]
State an estimate of the standard deviation of the heights.[1]
Explain why the mean height and standard deviation in part (ii) and part (iii) are estimates.[1]
Five students have transferred out of the class. The estimated mean height of the students in the class is now 163 cm. Explain what this tells you about the mean heights of the five students who transferred out.[1]
Height (\(x\) cm)
Frequency
\(140<x\leq150\)
\(3\)
\(150<x\leq160\)
\(10\)
\(160<x\leq170\)
\(7\)
\(170<x\leq180\)
\(4\)
\(180<x\leq190\)
\(1\)
A bag contains 5 red, 7 blue and 3 yellow identical balls.
One ball is selected at random. Find the probability that it is a yellow ball.[1]
Two balls are selected at random without replacement. Find the probability that both balls are of different colours.[2]
Three balls are selected at random, with replacement. Find the probability that two red balls and one blue ball are chosen.[3]
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Answer:(a)(i) \(150<x\le160\) (a)(ii) \(161\text{ cm}\) (a)(iii) \(10.2\text{ cm}\) (a)(iv) Grouped data use midpoints (a)(v) Mean below \(161\text{ cm}\) (b)(i) \(\frac15\) (b)(ii) \(\frac{71}{105}\) (b)(iii) \(\frac7{45}\)