Math Is Fun Forum

calc2

Guest

statistics

the weight of coconuts is normally distributed. it is proposed that the mean weight of ripe coconuts is 450g with a standard deviation of 45g. The mean weight of green coconuts is 420g with a standard deviation of 35g.
Question:
you find a coconut weighing 430gms. Using Z-scores or otherwise, show clearly how you would determine which type of coconut is it more likely to be.

Any help with this would be greatly appreciated.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: statistics

You don't need Z-scores for this. You just need to know that the fewer standard deviations away from the mean something is, the more common it will be.

If it was a ripe coconut, it would be 20g away from the mean, and so 20/45 standard deviations away from the mean.

Similarly, if it was a green coconut it would be 10/35 standard deviations away.

This second number is smaller, so the coconut you found is more likely to be green than ripe.

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Why did the vector cross the road?
It wanted to be normal.