please help with def The amount of pollutants that are found in waterways near large cities is normally distributed with mean9.4 ppm and standard deviation 1.4 ppm. 6 randomly selected large cities are studied. Round all answers to4 decimal places where possible.a. What is the distribution of X? X - N(b. What is the distribution of x? a - N(c. What is the probability that one randomly selected city's waterway will have more than 8.7 ppmpollutants?d. For the 6 cities, find the probability that the average amount of pollutants is more than 8.7 ppm.e. For part d), is the assumption that the distribution is normal necessary? O YesO Nof. Find the IQR for the average of 6 cities.Q1 =ppmQ3 =ppmIQR:ppm

Suppose, X be the amount of pollutants that are found in waterways near large cities. X follows Normal distribution with mean μ=9.4 and standard deviation σ=1.4.d. X¯=16∑i=16Xi follows Normal distribution with mean μ=9.4 and standard deviation σ=1.46=0.5715. The probability that the average amount of pollutants is more than 8.7. =PX¯≥8.7=PX¯-9.40.5715≥8.7-9.40.5715=PZ≥-1.2248, Z=X¯-9.40.5715~Normal(0,1)=PZ≤1.2248, Z =D-Z=Φ(1.2248) =0.8897, the value of Φ(1.2248) is taken from Normal distribution table. Therefore, The probability that the average amount of pollutants is more than 8.7 is 0.8897.e. Here, X1, X2,... X6 are Normally distributed. By the property of Normal distribution, ∑i=16Xi follows Normal distribution. Again by the property of Normal distribution 16∑i=16Xi follows Normal distribution. Therefore, this is a necessary assumption.f. Suppose q1 be the first quartile, PX¯≤q1=0.25⇒PX¯-9.40.5715≤q1-9.40.5715=0.25⇒PZ≤q1-9.40.5715=0.25, Z=X¯-9.40.5715~Normal(0,1) From Normal distribution table PZ≤-0.6745=0.25,⇒ q1-9.40.5715=-0.6745⇒q1=9.0145. Therefore the first quartile Q1=9.0145. Suppose q3 be the third quartile, PX¯≤q3=0.75⇒PX¯-9.40.5715≤q3-9.40.5715=0.75⇒PZ≤q3-9.40.5715=0.75, Z=X¯-9.40.5715~Normal(0,1) From Normal distribution table PZ≤0.6745=0.75,⇒ q3-9.40.5715=0.6745⇒q3=9.7855. Therefore the third quartile Q3=9.7855. Then, the interquartile range is IQR=Q3-Q1=9.7855-9.0145=0.771 Therefore, the IQR for the average of 6 cities is 0.771.