Given/Gegee: Z ~ N ( 0 , 1); Calculate: / Bereken:

Question

2.1 P(- 2.58 < Z < 2.52)

2.2 The value of k in. / Die waarde van k in. P(Z < k) = 0.9881

2.3 P(- 2.18 < Z < -1.82)

2.4 The value of k in. / Die waarde van k in. P(Z > k) = 0.9616

2.5 P(Z>1.82)

2.6 P(Z< -1.68)

2.7 P(0< Z<1.59)

Answer 1

2.1 P(- 2.58 < Z < 2.52) = P(Z < 2.52) - P(Z < -2.58)
= 0.9945 - 0.0049
= 0.9896

2.2 The value of k in. / Die waarde van k in. P(Z < k) = 0.9881
P(Z < k) = 0.9881
From standard normal distribution table, the value of k is approximately 2.3328

2.3 P(- 2.18 < Z < -1.82) = P(Z < -1.82) - P(Z < -2.18)
= 0.0344 - 0.0359
= 0.0015

2.4 The value of k in. / Die waarde van k in. P(Z > k) = 0.9616
P(Z > k) = 0.9616
P(Z < k) = 1 - 0.9616 = 0.0384
From standard normal distribution table, the value of k is approximately 1.7992

2.5 P(Z>1.82) = 1 - P(Z < 1.82)
= 1 - 0.9656
= 0.0344

2.6 P(Z< -1.68) = 0.0465

2.7 P(0< Z<1.59) = P(Z < 1.59) - P(Z < 0)
= 0.9441 - 0.5
= 0.4441