5 questions in pictures Normal Distribution

Normal distribution. Graphs, standard deviation, percentages, mean, using variable x. 5 questions in pictures.

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A set of exam scores are approximately normally distributed with mean = 66 and standard deviation = 5.
Use the Empirical Rule to determine the area of the shaded regions shown below.
51
56
61
71
76
81
66
Exam Scores
1
.
%
51
56
61
71
76
81
66
Exam Scores
2.
%
51
56
61
71
76
81
66
Exam Scores
نما
%
The distribution of weights for newborn babies is approximately normally distributed with a mean of 7.3 pounds and a standard deviation of 0.8 pounds.
Use the Empirical Rule to complete the statements below.
1. What percent of newborn babies weigh more than 8.1 pounds?
%
2. The middle 95% of newborn babies weigh between
and
pounds.
3. What percent of newborn babies weigh less than 5.7 pounds?
%
4. Approximately 50% of newborn babies weigh more than
pounds.
5. What percent of newborn babies weigh between 6.5 and 9.7 pounds?
%
A variable x is normally distributed with mean 18 and standard deviation 3.
Round your answers to the nearest hundredth as needed.
a) Determine the z-score for 2 = 20.
z =
b) Determine the 2-score for 2 = 13.
2=
c) What value of has a z-score of 3.33?
d) What value of x has a z-score of -0.7?
=
e) What value of x has a z-score of 0?
2=
The weights of a certain dog breed are approximately normally distributed with a mean of u = 52 pounds, and a standard deviation of o = 5 pounds.
Fill in the indicated boxes.
u=52
o= 5
u – 30 -20 to
utou+20 u +30
A dog of this breed weighs 48 pounds. What is the dog’s Z-score? Round your answer to the nearest hundredth as needed.
A dog has a z-score of 0.87. What is the dog’s weight? Round your answer to the nearest tenth as needed.
pounds
A dog has a z-score of -0.87. What is the dog’s weight? Round your answer to the nearest tenth as needed.
pounds
The lengths of mature trout in a local lake are approximately normally distributed with a mean of u = 12.1 inches, and a standard deviation of o = 1.8 inches.
Fill in the indicated boxes.
u= 12.1
0 = 1.8
u-30
-20
uro
u
u+O
u +20 + 30
Find the Z-score corresponding to a fish that is 12.9 inches long. Round your answer to the nearest hundredth as needed.
z=
How long is a fish that has a z-score of 0.8? Round your answer to the nearest tenth as needed.
inches