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in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257
? Related: Summary - Theoretical Distribution
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in a sample of 800 students the mean weight and standard deviation of ...
Solution:
Theoretical Distribution
The normal distribution is a theoretical distribution that is continuous and symmetrical. It is also known as the Gaussian distribution or the bell curve. The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean is the central point of the distribution, and the standard deviation measures the spread of the distribution.
Calculating the Number of Students Weighing Between 46kg and 62kg
To calculate the number of students weighing between 46kg and 62kg, we need to find the z-scores for these weights. The z-score is the number of standard deviations a data point is from the mean. We can use the formula:
z = (x - μ) / σ
where x is the weight, μ is the mean weight, and σ is the standard deviation of weight.
For x = 46kg:
z = (46 - 50) / 20 = -0.2
For x = 62kg:
z = (62 - 50) / 20 = 0.6
Now, we need to find the area under the normal curve between z = -0.2 and z = 0.6. We can use the standard normal distribution table or a calculator to find these areas. From the given information, we know that:
Area between z = 0 to z = 0.20 = 0.0793
Area between z = 0 to z = 0.60 = 0.2257
To find the area between z = -0.2 and z = 0.6, we can subtract the area between z = 0 and z = -0.2 from the area between z = 0 and z = 0.6:
Area between z = -0.2 and z = 0.6 = Area between z = 0 and z = 0.6 - Area between z = 0 and z = -0.2
= 0.2257 - 0.0793
= 0.1464
This area represents the proportion of students weighing between 46kg and 62kg. To find the number of students, we can multiply this proportion by the total number of students:
Number of students weighing between 46kg and 62kg = 0.1464 x 800
= 117.12
Therefore, there are approximately 117 students weighing between 46kg and 62kg.
Theoretical Distribution
The normal distribution is a theoretical distribution that is continuous and symmetrical. It is also known as the Gaussian distribution or the bell curve. The normal distribution is characterized by two parameters: the mean (μ) and the standard deviation (σ). The mean is the central point of the distribution, and the standard deviation measures the spread of the distribution.
Calculating the Number of Students Weighing Between 46kg and 62kg
To calculate the number of students weighing between 46kg and 62kg, we need to find the z-scores for these weights. The z-score is the number of standard deviations a data point is from the mean. We can use the formula:
z = (x - μ) / σ
where x is the weight, μ is the mean weight, and σ is the standard deviation of weight.
For x = 46kg:
z = (46 - 50) / 20 = -0.2
For x = 62kg:
z = (62 - 50) / 20 = 0.6
Now, we need to find the area under the normal curve between z = -0.2 and z = 0.6. We can use the standard normal distribution table or a calculator to find these areas. From the given information, we know that:
Area between z = 0 to z = 0.20 = 0.0793
Area between z = 0 to z = 0.60 = 0.2257
To find the area between z = -0.2 and z = 0.6, we can subtract the area between z = 0 and z = -0.2 from the area between z = 0 and z = 0.6:
Area between z = -0.2 and z = 0.6 = Area between z = 0 and z = 0.6 - Area between z = 0 and z = -0.2
= 0.2257 - 0.0793
= 0.1464
This area represents the proportion of students weighing between 46kg and 62kg. To find the number of students, we can multiply this proportion by the total number of students:
Number of students weighing between 46kg and 62kg = 0.1464 x 800
= 117.12
Therefore, there are approximately 117 students weighing between 46kg and 62kg.
Community Answer
in a sample of 800 students the mean weight and standard deviation of ...
N = 800, m= 50, SD = 20
no. of students whose weight between 46 kg 62 kg
P( 46 - 50/20 < x="" />< 62="" -="" 50="" />
P (-0.2 < x="" />< 0.6="" />
0.6 - [ 1 - (0.2) ]
0.7257 - [ 1- 0.5793 ]
0.7257 - 0.4207
0.305
number of students = 800 * 0.305
= 244
no. of students whose weight between 46 kg 62 kg
P( 46 - 50/20 < x="" />< 62="" -="" 50="" />
P (-0.2 < x="" />< 0.6="" />
0.6 - [ 1 - (0.2) ]
0.7257 - [ 1- 0.5793 ]
0.7257 - 0.4207
0.305
number of students = 800 * 0.305
= 244
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in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution?
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in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution? for CA CPT 2024 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution? covers all topics & solutions for CA CPT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution?.
in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution? for CA CPT 2024 is part of CA CPT preparation. The Question and answers have been prepared according to the CA CPT exam syllabus. Information about in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution? covers all topics & solutions for CA CPT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for in a sample of 800 students the mean weight and standard deviation of weight are found to be 50 kg and 20 kg .on the assumption of normality what is the number of students weighing between 46kg and 62kg?given area of the standard deviation normal 6 curve between z=0 to z=0.20=0.0793 and area between z=0 to z=0.60=0.2257 Related: Summary - Theoretical Distribution?.
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