Cat behavior: A report stated that the average number of times a cat returns to it's good bowl during the day is 37. Assuming the variable is normally distributed with a standard deviation of 3, what is the probability that a cat would return to it's dish between 34 and 39 times a day. Use the graphing calculator. Round the answer to four decimal places. P (34<X<39) =?

P (34<X<39) = 0.5899

Step-by-step explanation:

When the distribution is normal, we use 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 question, we have that:

What is the probability that a cat would return to it's dish between 34 and 39 times a day.

This is the pvalue of Z when X = 39 subtracted by the pvalue of Z when X = 34. So

X = 39

has a pvalue of 0.7486

X = 34

has a pvalue of 0.1587

0.7486 - 0.1587 = 0.5899

So

P (34<X<39) = 0.5899

-362

step-by-step explanation:

(12)(4)+2(12)-34(12)+2(12)-3

  \/         \/         \/         \/

  48 +   24 -   408 + 24 - 3

      \   /               \   /

          72     -     432 - 3 = -363