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The weights of a population of mice fed on a certain diet since birth are assumed to be normally distributed with μ = 100 and σ = 20 (measurement in grams). Suppose that a random sample of n = 4 mice is taken from this population. Find the probability thata exactly two weigh between 80 and 100 grams and exactly one weighs more than 100 grams.b all four mice weigh more than 100 grams.

Sagot :

The binomial distribution can be used to determine the likelihood that exactly two mice weigh between 80 and 100 grams and exactly one mouse weighs more than 100 grams.

a) The likelihood that a single mouse weighs between 80 and 100 grams is the same as the likelihood that it weighs between 80 and 100 grams and less than that. This is determined by the normal distribution's cumulative distribution function (CDF), which has a mean of 100 and a standard deviation of 20, and is assessed at 100 and 80, respectively. One less than the CDF of the normal distribution with a mean of 100 and a standard deviation of 20, evaluated at 100, yields the likelihood that a single mouse weighs more than 100 grams. The binomial probability mass function,

with parameters, n = 4

k = 2,

p = probability

that a single mouse weighs between 80 and 100 grams, then provides the likelihood that precisely two mice weigh between 80 and 100 grams and precisely one weighs more than 100 grams. The binomial probability mass function, with parameters, n = 4,

k = 4

p = probability

that a single mouse weighs more than 100 grams, provides the likelihood that all four mice weigh more than 100 grams.

b) We are unable to compute the probabilities precisely because we do not have the values of the CDF for the normal distribution. However, it is possible to state that the likelihood of all four mice weighing more than 100 grams is less likely than the likelihood that two mice exactly weigh between 80 and 100 grams and one mouse precisely weighs more than 100 grams. This is so because it is less likely that a single mouse will weigh more than 100 grams than it is that it will weigh between 80 and 100 grams.

To learn more about probability: https://brainly.com/question/13604758

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