Scores on exam2 for statistics are normally distributed with

Scores on exam-2 for statistics are normally distributed with mean 70 and standard deviation 15.

a) Find P(55 < x < 67)

b) Find a, if P (x < a) = 0.9505

c) Find P (x > 64)

d) If 49 students are considered, what is the probability that the average score of these students is between 55 and 67 points?

i)P(55 < X < 67) = P( -1 < Z < -0.2) = 0.2620 (From the z table)

ii) a = 70 + 1.65 * 15 = 94.75

iii) P(X > 64) = P(Z > -0.4) = 0.6554 (From z table)

iv) Required probability = P(-7 < z < -1.34) = 0.0901 (From z table)