Question

Heights of 360 children are normally distributed with mean 120cms. and variance 4cms. Find the expected number of children having heights i) greater than 118cms. ii) between 116cms, and 119cms. iii) less than 117cms. uu​

Answer 1

Answer:

i) 303 (approximately)

ii) 124 (approximately)

iii) 24 (approximately)

Step-by-step explanation:

Given:

Mean height, μ = 120 cm

Variance, σ^2 = 4 cm^2

We can find the standard deviation using the formula: σ = √(σ^2)

So, σ = √4 = 2 cm

i) To find the number of children with height greater than 118 cm, we need to find the area to the right of 118 cm in the normal distribution curve. 

Z-score for 118 cm can be calculated as: Z = (118 - 120) / 2 = -1

Using the standard normal distribution table or calculator, we can find the area to the right of Z = -1 which is 0.8413. This means that 84.13% of the children have heights greater than 118 cm.

Expected number of children with heights greater than 118 cm = 0.8413 x 360 = 303 (approximately)

ii) To find the number of children with height between 116 cm and 119 cm, we need to find the area between these two values in the normal distribution curve.

Z-score for 116 cm can be calculated as: Z = (116 - 120) / 2 = -2

Z-score for 119 cm can be calculated as: Z = (119 - 120) / 2 = -0.5

Using the standard normal distribution table or calculator, we can find the area between Z = -2 and Z = -0.5 which is 0.3446. This means that 34.46% of the children have heights between 116 cm and 119 cm.

Expected number of children with heights between 116 cm and 119 cm = 0.3446 x 360 = 124 (approximately)

iii) To find the number of children with height less than 117 cm, we need to find the area to the left of 117 cm in the normal distribution curve.

Z-score for 117 cm can be calculated as: Z = (117 - 120) / 2 = -1.5

Using the standard normal distribution table or calculator, we can find the area to the left of Z = -1.5 which is 0.0668. This means that 6.68% of the children have heights less than 117 cm.

Expected number of children with heights less than 117 cm = 0.0668 x 360 = 24 (approximately)

To know more about the expected number of children having heights refer:

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