Question

Suppose x is a normally distributed random variable with 13 and Find each of the following probabilities Click here to view a table of areas under the standardized normal curve. a. P(x 2 14.5)-(Round to three decimal places as needed) b. P(x s11)=L 1 (Round to three decimal places as needed.) c. P(13 66ss 17.8)= ] (Round to three decimal places as needed) d. P(7.96 srs 15 44)= (Round to three decimal places as needed.) Enter your answer in each of the answer boxes

Answer 1

μ = 13

σ = 2

a) $P(X > 14.5) = P(\frac{X-\mu}{\sigma}>\frac{14.5-\mu}{\sigma})$

                                  $= P(Z>\frac{14.5-13}{2})$

                                  = P(Z > 0.75)

                                  = 1 - P(Z < 0.75)

                                  = 1 - 0.7734

                                  = 0.227

b) $P(X <11) = P(\frac{X-\mu}{\sigma}<\frac{11-\mu}{\sigma})$

                              $= P(Z<\frac{11-13}{2})$

                              = P(Z < -1)

                              = 0.159

c) $P(13.66<X<17.8)=P(\frac{13.66-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{17.8-\mu}{\sigma})$

                                                    $=P(\frac{13.66-13}{2}<Z<\frac{17.8-13}{2})$

                                                    = P(0.33 < Z < 2.4)

                                                    = P(Z < 2.4) - P(Z < 0.33)

                                                    = 0.9918 - 0.6293

                                                    = 0.363

d) $P(7.96<X<15.44)=P(\frac{7.96-\mu}{\sigma}<\frac{X-\mu}{\sigma}<\frac{15.44-\mu}{\sigma})$

                                                    $=P(\frac{7.96-13}{2}<Z<\frac{15.44-13}{2})$

                                                    = P(-2.52 < Z < 1.22)

                                                    = P(Z < 1.22) - P(Z < -2.52)

                                                    = 0.8888 - 0.0059

                                                    = 0.883