What is the "grand" mean and standard deviation of these 1,000 means? Does the grand mean closely approximate(on a relative basis) the mean of the original distribution?Does this confirm the second part of the central theorem why or why not

Step 7: Mean and the standard deviation of the sample mean distribution Now you will calculate the "grand" mean ("grand" because it is the mean of the 1,000 means) and the standard deviation of 1,000 sample means. Note that the distribution of sample means was approximately Normal (bell-shaped) in Step 6. Therefore, calculating the mean and the standard deviation of this distribution will allow us to calculate probabilities and critical values Click the block of code below and hit the Run button above In [10]: H # calculate mean of the 1, 000 sample means ( this is called the grand mean or mean of the means). mean1000 = means_of [ ' means ' ]. mean( ) print("Grand Mean (Mean of 1000 sample means ) =", round (mean1060, 2) ) # calculate standard deviation of the 1, 000 sample means. std1000 = means_df [ 'means' ]. std( ) print("Std Deviation of 1000 sample means =", round (std1000, 2) ) # print the probability that a specific mean is 450 or Less for a Normal distribution with mean and standard deviation of 1, prob_450_less_or_equal = st. norm. cdf(450, mean1000, std1000) print("Probability that a specific mean is 450 or less =", round(prob_450_less_or_equal, 4) ) Grand Mean (Mean of 1000 sample means ) = 491.15 Std Deviation of 1000 sample means = 50.05 Probability that a specific mean is 450 or less = 0.2055