Question

Pregnancy Length in a Population of New Mothers 282 <x< 293 = 269 = 11 х 239 282 293 Pregnancy length (in days)

find the probability that the member selected at random is from the shaded area of the graph (round to four decimal places as needed)

please solve

Answer 1

Step 1: Sketch the curve. The probability that 282 < X < 293 is equal to the blue area under the curve. 0.045 0.040 0.035 0.030 0.025 y 0.020 0.015 0.010 0.005 0.000 282 293 -0.005 230 235 240 245 250 255 260 265 270 275 280 285 290 295 300 305 х

Step 2: Since u = 269 and o=11 we have: 282 – 269 X-u P ( 282 < X < 293 ) = P ( 282 – 269 < X – u < 293 – 269 ) =P 293 – 269 11 11 o Since Z = 1541 282-269 11 -1.18 and 293–269 2.18 we have: 11 P ( 282 < X < 293 ) =P (1.18 <<2.18) Step 3: Use the standard normal table to conclude that: P (1.18 <3 < 2.18 ) = 0.1044