99.6% for
68.2%
True.
No, but the approximation is better for normally distributed variables.
A particular fruit's weights are normally distributed, with a mean of 760 grams and a standard deviation of 15 grams. If you pick one fruit at random, what is the probability that it will weigh between 722 grams and 746 grams-----A particular fruit's weights are normally distributed, with a mean of 567 grams and a standard deviation of 25 grams.
67% as it's +/- one standard deviation from the mean
About 98% of the population.
68.2%
The Z test.
The mean and standard deviation. If the data really are normally distributed, all other statistics are redundant.
True.
No, but the approximation is better for normally distributed variables.
Also normally distributed.
A particular fruit's weights are normally distributed, with a mean of 760 grams and a standard deviation of 15 grams. If you pick one fruit at random, what is the probability that it will weigh between 722 grams and 746 grams-----A particular fruit's weights are normally distributed, with a mean of 567 grams and a standard deviation of 25 grams.
The answer depends on what SAT tests. In the UK the mean is 100 and the SD approx 15 - the scores are truncated at 100 +/- 44.
square (25/36) = 5/6 = .833
According to the Central Limit Theorem, even if a variable has an underlying distribution which is not Normal, the means of random samples from the population will be normally distributed with the population mean as its mean.
No. The variance of any distribution is the sum of the squares of the deviation from the mean. Since the square of the deviation is essentially the square of the absolute value of the deviation, that means the variance is always positive, be the distribution normal, poisson, or other.