Let Z be a N (0.1). Determine the following probabilities a) P (-1.5 <Z<1,5) b) P (Z<0,2) c) P(0<2<2,5) d) P(Z> -2.5)

a) P(-1.5 < Z < 1.5)

1. For a standard normal distribution, calculate the cumulative distribution function (CDF):
P(Z < 1.5) - P(Z < -1.5)

2. Using standard normal distribution tables or a calculator:
P(Z < 1.5) = 0.9332
P(Z < -1.5) = 0.0668

3. Then:
P(-1.5 < Z < 1.5) = 0.9332 - 0.0668 = 0.8664

Answer: 0.8664

b) P(Z < 0.2)

1. Directly use the CDF for standard normal distribution for:
P(Z < 0.2) = 0.5793

Answer: 0.5793

c) P(0.2 < Z < 2.5)

1. For a standard normal distribution, calculate:
P(Z < 2.5) - P(Z < 0.2)

2. Using standard normal distribution tables or a calculator:
P(Z < 2.5) = 0.9938
P(Z < 0.2) = 0.5793

3. Then:
P(0.2 < Z < 2.5) = 0.9938 - 0.5793 = 0.4145

Answer: 0.4145

d) P(Z > -2.5)

1. Use the complement rule for the CDF of a standard normal distribution:
1 - P(Z < -2.5)

2. Using standard normal distribution tables or a calculator:
P(Z < -2.5) = 0.0062

3. Then:
P(Z > -2.5) = 1 - 0.0062 = 0.9938

Answer: 0.9938