Business Statistics II Assume thatz is a datavalue from a standard normal distri

Question

Business Statistics II

Assume thatz is a datavalue from a standard normal distribution. Find P(z -0.50), the area under the standard normal curve to the right of z =-0.50 QUESTION 3 Assume that z is a data value from a standard normal distribution. Find P(76 153), the area under the standard normal curve to the left of z = 1.53. QUESTION Assume that zisa data value from a standard normal distribution. Find P(z > 1.53), the area under the standard normal curve to the right of z = 1.53. QUESTION5 Assume that z is a data value from a standard normal distribution. Find P(-0.5

Explanation / Answer

1) By symmetry
P(Z < -0.50) = P(Z > 0.50) = 1 - P(Z < 0.50)
= 1 - 0.69146
= 0.30854

2) P(Z > -0.5) = P(Z < 0.5) = 0.6915

3) P(Z < 1.53) = 0.93699

4) P(Z > 1.53) = 1 - P(Z < 1.53) = 1 - 0.93699 = 0.06301

5) P(-0.50 < Z < 1.53) = P(Z < 1.53) - P(Z < -0.50) = 0.93699 - 0.30854 = 0.62845

6) P(X<20) = P ( Z < (20 - 21.4 / 6 )) = P (Z < (-1.4 / 6 )) = P ( Z < -0.23 ) = 1 - P(Z>0.23) = 1- 59095 = 0.40905

7) P(X > 30) = P ( Z > (30 - 21.4 / 6 )) = P ( Z > (8.6 / 6 )) = P ( Z > 1.43) = 1 - P ( Z < 1.43) = 1 - 0.92364 = 0.07636

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