In the diagram below, the angle of depression from the top of the lighthouse to a speed boat is 27 degrees. The base of the lig
hthouse is 33 ft away from the boat. Determine the height of the lighthouse, to the nearest tenth of a foot.
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The z-score of the considered newborn having 4,000 g weight is
If we've got a normal distribution, then we can convert it to standard normal distribution and its values will give us the z score.
If we have
(X is following normal distribution with mean and standard deviation
)
then it can be converted to standard normal distribution as
(Know the fact that in continuous distribution, probability of a single point is 0, so we can write
Also, know that if we look for Z = z in z tables, the p value we get is
For the considered case, the statement in the problem is missing the mean weight of the newborn and standard deviation of the data set of weights of newborn.
Thus, for them, we can consider variables in place of their actual values.
Let we have:
- X = weights of newborns for some considered system (in grams)
= mean weight of newborns (in grams)
= standard deviation of the data set of weights of newborns
Then, the z-score for X = 4000 is
Thus, the z-score of the considered newborn having 4,000 g weight is
Learn more about z-scores here: