Answer:
Part A:
No, it is not possible to accurately calculate the probability that the mean picture size is more than 3.8MB for an SRS of 20 pictures. This is because the Central Limit Theorem, which states that the distribution of sample means approaches a normal distribution as the sample size increases, only applies when the sample size is large (typically defined as 30 or more). With a sample size of 20, the distribution of sample means is not likely to be normal, and it is therefore not appropriate to use the normal distribution to calculate probabilities.
Part B:
The Central Limit Theorem allows us to find the probability that the mean picture size is more than 3.8MB by assuming that the distribution of sample means will be approximately normal, even though the distribution of individual picture sizes is not necessarily normal. To calculate this probability, we can use the following steps:
Calculate the mean and standard deviation of the sample means:
Mean: 3.7MB
Standard deviation: (0.78MB) / sqrt(60) = 0.13MB
Standardize the value of 3.8MB by subtracting the mean and dividing by the standard deviation:
(3.8MB - 3.7MB) / 0.13MB = 0.77
Use a standard normal table or a calculator to find the probability that a standard normal random variable is greater than 0.77. This probability is approximately 0.22.
Therefore, the probability that the mean picture size is more than 3.8MB for a sample of 60 pictures is approximately 0.22.