Question

hi is my answer right if not please check it thank you

Astrophysicists investigating the solar system find a group of potentially hazardous 'near Earth objects' (NEOs) within the asteroid belt. They find the diameter of these NEOs has a mean of 1.75km and standard deviation 0.5km. Assuming the diameters are Normally distributed, what is the probability that for a randomly selected NEO amongst the group, the diameter is: Note: Only put final answers and all answers must be in 4 decimal place format i.e. (0.0000) 1. at least 1.89km. 0.3897 between 1.76km and 1.8km. 0.0318 [6]

Answer 1

Yi - x = 175, 5=015, 2= *- ~N(0,1) (1) P(x2,1889) = P(Z > 1.89 – 1975) 0.5 =P(22 0.289 = P(ZE-0.28) -> Symmetic about mean = NORMSDIST (-0.28) = 10.3897 Ⓡ P (1.76 < x <1.80) = P(x<1.80) -P(XC1.789 = P(Z < 1.3.-4;) -PLZ < 1.76-475) 0.5 0.5 / = P(Z <0.10) - PIZ < 0.02) = NORMS DIST (0.10) - Norms Dist 10.02) = = 0.5398 – 0.508 0 0.0318

Your answers are correct