Hil Connect Math onnect MATH tos by ALEKS Corp Final Exam Previous 21 22| 24 25

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Hil Connect Math onnect MATH tos by ALEKS Corp Final Exam Previous 21 22| 24 25 26 27 28 29 30 Next Question 23 of 36 (1 point) A report stated that the average number of times a cat returns to its food bowl during the day is 35. Assuming the variable is normally distributed with a standard deviation of 4, what is the probability that a cat would return to its dish between 33 and 38 times a day? Round the final answer to four decimal places and intermediate z value caleulations to two decimal places. P(33

Explanation / Answer

23.

NORMAL DISTRIBUTION
the PDF of normal distribution is = 1/ * 2 * e ^ -(x-u)^2/ 2^2
standard normal distribution is a normal distribution with a,
mean of 0,
standard deviation of 1
equation of the normal curve is ( Z )= x - u / sd ~ N(0,1)
mean ( u ) = 35
standard Deviation ( sd )= 4

a.
probability that a cat would return to its dish between 33 and 38 times a day
To find P(a < = Z < = b) = F(b) - F(a)
P(X < 33) = (33-35)/4
= -2/4 = -0.5
= P ( Z <-0.5) From Standard Normal Table
= 0.3085
P(X < 38) = (38-35)/4
= 3/4 = 0.75
= P ( Z <0.75) From Standard Normal Table
= 0.7734
P(33 < X < 38) = 0.7734-0.3085 = 0.4648

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