Question

The mass of plants in a botany lab are normally distributed with a mean of 54 grams and a standard deviation of 6.5 grams. Use this to compute : a. The probability that one randomly chosen plant will have a mass that less than 49.25 grams b. The probability that one randomly chosen plant will have a mass that is between 52 grams and 62 grams. c. The mass of a plant which weighs less than the top 15% of plants in the lab. d. The probability that 25 randomly chosen plants will have a mean mass of no more than 50 grams

Answer 1

µ = 54

sd = 6.5

a)

                                   

                                    = P(Z < -0.73)

                                    = 0.2327

b)

                                        

                                         = P(-0.31 < Z < 1.23)

                                         = P(Z < 1.23) - P(Z < -0.31)

                                         = 0.8907 - 0.3783

                                         = 0.5124

c)

or, x = 54 - 1.04 * 6.5

or, x = 47.24

d) n = 25

                         

                          = P(Z < -3.08)

                          = 0.001