A population has mean 75 and standard deviation 12 . a) Random samples of size 121 are taken. Find the mean and standard deviation of the sample mean. [Ans \( \mu_{\bar{x}}=75 ; \sigma_{\bar{x}}=1.09 \) ] b) How would the answers to part (a) change if the size of the samples were 400 instead of 121 ? [Ans \( \mu_{\bar{x}} \) stays the same but \( \sigma_{\bar{x}} \) decreases to 0.6 ]

2) Bestain \( f(2)=10 \)

Questions An um contains 5 white and 3 black bells. Two balls are drawn at random without replacement. If X denotes the number of white balls, then find the probability deribution of X .

cercice 2 (un peu de trigonométrie hyperbolique) 1. a) Montrez que l'équation \( 2 \operatorname{sh}(x)+1=0 \) admet une unique solution sur \( \mathbb{R} \). On note a cette solution (bien qu'elle soit calculable, il n'est pas nécessaire d'avoir l'expression exacte pour continuer cet exercice) b) Justifiez que la fonction \( u: x \mapsto \operatorname{ch}^{2} x+\operatorname{sh} x \) est dérivable et montrez que pour tout réel \( x, \operatorname{ch}^{2} x+\operatorname{sh} x \geq 0 \)

Write the places of work. 1 A director works in a 2 A 3 A 5 A hairdresser works in o 6 You con buy lots of different things in a

5. Elaine had 1 m 70 cm of wire. She used it to form a square of area \( 100 \mathrm{~cm}^{2} \) and a rectangle of area \( 384 \mathrm{~cm}^{2} \). The breadth of the rectangle was 16 cm . How much wire did she have left?