Final answer:
To compute probabilities in a standard normal distribution, we can use the z-table. For example, the probability that Z<2.60 is approximately 0.9953. The probability that Z>0.04 is approximately 0.4840.
Step-by-step explanation:
For the given question, we need to compute the probabilities associated with specific values in a standard normal distribution.
a) P(Z<2.60)
To find the probability that a standard normal random variable is less than 2.60, we look up the value 2.60 in the z-table and find the corresponding probability, which is approximately 0.9953.
b) P(Z>0.04)
To find the probability that a standard normal random variable is greater than 0.04, we subtract the probability of being less than 0.04 from 1. The probability of being less than 0.04 can be found by looking up the value 0.04 in the z-table, which is approximately 0.5160. Therefore, the probability of being greater than 0.04 is approximately 1 - 0.5160 = 0.4840.
c) P(-1.66<Z<0.43)
To find the probability that a standard normal random variable is between -1.66 and 0.43, we subtract the probability of being less than -1.66 from the probability of being less than 0.43.
The probability of being less than -1.66 can be found by looking up the value -1.66 in the z-table, which is approximately 0.0475.
The probability of being less than 0.43 can be found by looking up the value 0.43 in the z-table, which is approximately 0.6664. Therefore, the probability of being between -1.66 and 0.43 is approximately 0.6664 - 0.0475 = 0.6189.
d) P(-0.18<Z<2.60)
To find the probability that a standard normal random variable is between -0.18 and 2.60, we subtract the probability of being less than -0.18 from the probability of being less than 2.60.
The probability of being less than -0.18 can be found by looking up the value -0.18 in the z-table, which is approximately 0.4286.
The probability of being less than 2.60 can be found by looking up the value 2.60 in the z-table, which is approximately 0.9953. Therefore, the probability of being between -0.18 and 2.60 is approximately 0.9953 - 0.4286 = 0.5667.
e) P(Z>0.43)
To find the probability that a standard normal random variable is greater than 0.43, we subtract the probability of being less than 0.43 from 1.
The probability of being less than 0.43 can be found by looking up the value 0.43 in the z-table, which is approximately 0.6664. Therefore, the probability of being greater than 0.43 is approximately 1 - 0.6664 = 0.3336.