Question

26-Suppose a simple random sample of size n=36 is obtained from a population with μ=64 and σ=15.

1- P(x->65.5) =

2- P(x->c) = 0.72. Find c.=

3- P(64.3<x-<65.65) =

4-P(|z|<c) = 0.45, Find c.=

5-P(|z|>c) = 0.35. Find c.=

Answer 1

Standard deviation of = 15 / = 2.5

1.

P(   65.5) = P(Z (65.5 - 64) / 2.5)= P(Z 0.6) = 0.2743 (Using Z tables)

2.

P( c) = 0.72

P(Z (c - 64) / 2.5) = 0.72

(c - 64) / 2.5 =   -0.5828 (Using Z tables)

c = 64 - 0.5828 * 2.5 = 62.543

3.

P(64.3< < 65.65) = P( < 65.65) - P( < 64.3)

= P(Z < (65.65 - 64) / 2.5) - P(Z < (64.3 - 64) / 2.5)

= P(Z < 0.66) - P(Z < 0.12)

= 0.7454 - 0.5478

= 0.1976

4.

P(|z|<c) = 0.45

P(-c < z < c) = 0.45

P(z < -c) + P(z > c) = 1 - 0.45 = 0.55

P(z > c) = 0.55 / 2 =  0.275 (Due to symmetry of normal distribution)

c = 0.5978 (Using z table)

5.

P(|z|>c) = 0.35

P(z < -c) + P(z > c) = 35

P(z > c) = 0.35 / 2 =  0.175 (Due to symmetry of normal distribution)

c = 0.9346 (Using z table)