Vehicle speed on a particular bridge in China can be modeled as normally distributed.USE SALT(a) If 5% of all vehicles travel less than 39.19 m/h and 10% travel more than 73.24 m/h, what are the mean and standard deviation of vehicle speed? (Round your answers to three decimal places.)meanstandard deviation(b) What is the probability that a randomly selected vehicle's speed is between 50 and 65 m/h? (Round your answer to four decimal places.)(c) What is the probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h? (Round your answer to four decimal places.)You may need to use the appropriate table in the Appendix of Tables to answer this question

Let X denote the vehicle speed on a particular bridge in China & X follows the normal distribution.We are asked to find the mean and standard deviation of the same using the given information.a) Mean and standard deviation: Given that 5% of all vehicles travel less than 39.19 and 10% of all vehicles travel more than 73.245% of all vehicles travel less than 39.19 m/hThe Z score corresponds to the area 0.05 is -1.6449So we can write this using the z score formula as,10% of all vehicles travel more than 73.24 m/hThe Z score corresponds to the area of 0.10 is 1.2816So we can write this using the z score formula as,Now we can solve the two equations to get µ and σ.Subtract equation (1) from (2) we get,Now we have standard deviation (σ) as 11.6351, insert this into equation (1) to get mean (µ).Here we have the mean (µ) as 58.3286Note: Please note that we have found the z values using the z table. You can find it in Excel by using = NORM.S.INV() function also.b) The probability that the randomly selected vehicle's speed is between 50 & 65: c) The probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h: Z tables for your information,a) Mean, µ=58.329 & standard deviation, σ=11.635b) The probability that the randomly selected vehicle's speed is between 50 m/h & 65 m/h is 0.4799c) The probability that a randomly selected vehicle's speed exceeds the speed limit of 70 m/h is 0.1587