Question

You are allowed to use Geogebra on this question. Heights of 10 year old children, regardless of gender assigned at birth, closely follow a normal distribution with mean 54.6 inches and standard deviation 6.8 inches. Round answers to 4 decimal places. a) What is the probability that a randomly chosen 10 year old child is less than 47.9 inches? b) What is the probability that a randomly chosen 10 year old child is more than 57.5 inches? c) What proportion of 10 year old children are between 49.7 and 60.6 inches tall? d) 90% of all 10 year old children are less than inches.

Answer 1

- Civen mian uz 54.6 inches Standard deviation 8.920 inches G (x247.9) 27 Istore = X-M for 42.5 Escoy 5.th 6.8 =-0.985 gs MON using standard stable P (2 2-0.99) P(x< curs) 0.16U (9 Escose for x=57.5 z = X-M 57.5-54-6 6-8 7 az 0.93

(x > > 57-5) = P(za >0-43) = 0.3336 ( Using Standard table) (ग 1-48X P 45.7 < x 560.6) ep Z ug. 7 -0.72 us. f -54.6 6.8 2 for 6o.b 72 bob-54.6 6.8 02.88 cu ug. 7 < X < 6ob d .o.92c z 20.88 naze ) p & <0.83) = 0-8108 P (22-072)=1 p( 220.72) - 1-0-7642 (table) =002358 p(-0.72€ 2 < 0.88 )= 0.8106-0.2358 -0.5748

а) х Х goy vale Z score a 1,232 . Хоч ха (х - (1 р. 2 |-232 x 6-8 теч. 6 2 63-3) 26 P(x63-376 ) - 0.9