Assume X has a normal distribution, with the specified meanand standard deviation. Find the indicated probabilities.

6. P(40 <= x <= 47) M = 50; s = 15

10. P(x >= 2); M = 3; s = 0.25

14. Find z such that 97.5% of the standard normal curve lies to the left of z.

18. Find z such that 95% of the standard normal curve lies to the right of z.

Please see the attached file.

6. P(40 <= x <= 47) M = 50; s = 15

Mean=M = 50

Standard deviation =s= 15

x1= 40

x2= 47

z1=(x1-M )/s= -0.6667 =(40-50)/15

z2=(x2-M )/s= -0.2 =(47-50)/15

Cumulative Probability corresponding to z1= -0.6667 is= 0.2525 0r= 25.25%

Cumulative …

Probability calculations have been made using Normal Distribution.