In an albatross colony the wingspan of the birds is approximately normally distributed with standard deviation 0.43 metres. in this colony, 67% of the birds have wingspan less than 3.21 metres. find the average wingspan of the birds in this colony. give your answer as a decimal, rounded to two decimal places. do not include the unit.

The answer is 3.02.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

67% of the birds have wingspan less than 3.21 metres.

This means that the pvalue of Z when X = 3.21 is 0.67. So when X = 3.21, Z = 0.44.

We have to find

Multiplying by -1

The answer is 3.02.

x is variable or an unknown value to find

example:

2x = 5 which means x = 3

the equation for this situation is y=122+45. to solve the equation you would add 45 and 122 to get a total of 167lbs. in conclusion, grace's weight eight weeks ago was 167lbs.