A particular fruit's weights are normally distributed, with a mean of 239 grams and a standard deviation of 7 grams. If you pick 11 fruit at random, what is the probability that their mean weight will be between 240 grams and 244 grams
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
A particular fruit's weights are
If you pick 11 fruit at random, what is the
Let is defined as the mean weight of fruit's which follows normal distribution. The mean is 239 grams, standard deviation is 7 grams, and sample size is 11.
The probability that their mean weight will be between 240 grams and 244 grams is,
The probability of z less than 2.3690 can be obtained using the excel formula “=NORM.S.DIST(2.3690,TRUE)”. The probability value is 0.9911.
The probability of z less than 0.4738 can be obtained using the excel formula “=NORM.S.DIST(0.4738,TRUE)”. The probability value is 0.6822.
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