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Elden [556K]
2 years ago
5

Suppose babies born in a large hospital have a mean weight of 3316 grams, and a standard deviation of 324 grams. If 83 babies ar

e sampled at random from the hospital, what is the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams?
Mathematics
1 answer:
Anuta_ua [19.1K]2 years ago
5 0

Answer: 0.129

Step-by-step explanation:

Let \overline{X} denotes a random variable that represents the mean weight of babies born.

Population mean : \mu= \text{3316 grams,}

Standard deviation: \text{324 grams}

Sample size = 83

Now, the probability that the mean weight of the sample babies would differ from the population mean by greater than 54 grams will be :

P(|\mu-\overline{X}|>54)=1-P(\dfrac{-54}{\dfrac{324}{\sqrt{83}}}

hence, the required probability =  0.129

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