Final answer:
To find the probabilities mentioned, we need the mean (μ) and standard deviation (σ) of the population. The sample size (n) is given as 64. We will assume that the population is normally distributed.
Step-by-step explanation:
In order to find the probabilities mentioned, we need the mean (μ) and standard deviation (σ) of the population. The sample size (n) is given as 64. We will assume that the population is normally distributed.
a) To find the probability that the sample mean will be larger than 1.2217, we need to calculate the z-score and then find the corresponding probability using a standard normal distribution table.
b) To find the probability that the sample mean will be less than 1.2297, we follow the same steps as in part (a).
c) To find the probability that the sample mean will be between 1.200 and 1.2137, we calculate the z-scores for the lower and upper bounds, and then subtract the corresponding probabilities.
d) To find the probability that the sample mean will be greater than 1.2007, we can use the same steps as in part (a).