The time taken by employees at Grace Floral shop to put a bouquet together has a normal distribution with mean 26.4 minutes and standard deviation 8 minutes. (i) Find the probability that an employee chosen at random takes between 24.6 and 27.8 minutes to put a bouquet together. (ii) 12% of employees take more than t minutes to put a bouquet together.Find the value of t.

Leave all probabilities as percentages, define x on all problems with data. Simple random samples of high interest (8.9%) and low interest (6.3%) mortgages were obtained. For the 40 high interest mortgages, the borrowers had a mean FICO credit score of 594.8 and a standard deviation of 12.2. For the 40 low interest mortgages, borrowers had a mean FICO credit score of 785.2 and a standard deviation of 16.3. Use an alpha level of 0.01, and a two tailed test of hypothesis to test the claim that the mean FICO score borrowers with a high interest mortgage is the same as the mean FICO score of borrowers with the low interest mortgage.

Suppose the weight of watermelons produced in Adana follows the normal distribution with mean 7.2 kg and standard deviation 2.4. Find the proportion of these watermelons that weight heavier than 7.5kg. If we randomly select one of these watermelons, find the probability that its weight will be less than 7kg.

Assume a light bulb has a burn life that is normally distributed with a mean of 159 hours and a standard deviation of 16 hours. Suppose you sample 30 bulbs and calculate a sample average (Y) burn life. Find the probability that a give bulb in the sample has a burn life greater than 163 hours.