Question

V. What percent of the pregnancies last between 266 and 282 days? vi. What percent of the pregnancies last fewer than 250 days? vii. What percent of the pregnancies last between 234 and 314 days? viii. How long are the longest 2.5% of pregnancies?

answer on v,vi,vii, and viii only

Answer 1

Solution: We have given X follows normal distnbution with mean = 266 days and standard deviation = 16 days V) P ( 266 x < 282) = P(X<282) - P(X<266) x-ul . 282 - 2661 (x-1 266-260) 16 / =P ( 221 ) - P(Z <0) - NORMSD TST (1) - NORMSDIST (0) = 0.8413 - 0.5 = 0.3413 pregnancies last between 266 and 28 2 days The percentage of is 34.13% vi) P(x<250) = u 250-266 P( 16 = P(Z <-1) : NORMSO IST (H) = 0.1587 fewer than 250 last pregnancies of The percentage days is 15.87%. vii) P ( 234 < x < 314) = P(a <314) - P(x < 234) =P(May < 3147266.) - PCV LC 2341264) = P(Z <3 ) - P(Z <-2) : NORMSDZST (3) - NORMSOIST(-2)

= 0.9987 -0.0228 last between = 0.9759 The percentage of the pregnancies 234 and 314 days in 97,59%. vill for this we want separates 2.5% of to the find the mark which area, to the right side (0.0250) or o. 9750 to the left. we choose z =1.96. In this case a we know, 2 = 02 tu 11 - 16 X 1.96 + 266 11 = 297.36 x 298 The longest 2.5% of pregnanies are 298 days.