Question

AVE 1537 AL JU 34 8 ce: W 3 Knowledge Check (due Day 51 Hele Toto is developing a new deluxe baby bassinet. If the length of a newborn baby is normally distributed with a mean of 50 cm and a standard deviation of so, what should be the north of the batt ensure that 99 percent of newborn babies will fit with a safety margin of 15 cm on each end of the bassinet? Multiple Choice 95 45 cm 85 22 cm O 9163 cm 98 92 cm Next > < Prev 6 of 10

Answer 1

$\text{Let X be a RV denoting the length of a new born. Then }\\ X\sim N(50,5)\\ \implies P((X-50)/5<z_{0.01})=99\%\\ \implies P((X-50)/5<2.33)=99\%\\ \implies P(X<61.65)=99\%\\ \text{Thus, without safety margins, a length of 61.65cm would do}\\ \text{Now, since we want 15cm margin on both ends, the length should be:}\\ 61.65+15+15 = 91.65cm\text{ (3rd Option)}$