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A particular fruit's weights are normally distributed, with a mean of 562 grams and a standard...

A particular fruit's weights are normally distributed, with a mean of 562 grams and a standard deviation of 28 grams. If you pick 17 fruit at random, what is the probability that their mean weight will be between 554 grams and 565 grams (Give answer to 4 decimal places.)

Math   Statistics-And-Probability   
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Answer #1

Solution :

Given that,

mean = = 562

standard deviation = = 28

= / n = 28 / 17 = 6.7910

= P[(554 - 562) /6.7910 < ( - ) / < (565 - 562) / 6.7910)]

= P(-1.1780 < Z < 0.4418)

= P(Z < 0.4418) - P(Z < -1.1780)

= 0.6707 - 0.1194

= 0.5513

Probability = 0.5513

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