Question

the weights of 1000 students are normally distributed with mean 40kg , standard deviation 4kg.find the number of students with weight 1) less than 50kg 2) between 40 and 45 kgs​

Answer 1

Step-by-step explanation:

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Answer 2

Answer:

1)Number of students with weight less than 50kg are 994

2)Number of students with their weights between 40-45kg are 394

Step-by-step explanation:

Given that,

The weights of 1000 students are normally distributed with mean 40kg , standard deviation 4kg.

Writing the given data in symbolical form

$n=1000\\\mu=40\\\sigma=4$

The statistic parameter Z is related to the mean and standard deviation as follows

$Z=\frac{X-\mu}{\sigma}$

1)less than 50kg

For this condition,X=50kg and by substituting this value in the statistic parameter we get

$Z < \frac{50-40}{4} = > Z < 2.5$

Now shall find $P(Z < 2.5)$ as shown

$P(Z < 2.5)=0.5+P(0 < Z < 2.5)=0.5+0.4938=0.9938$

Hence number of students with weight less than 50kg are

$0.9938\times1000=993.8\approx994$

2)Between 40 and 45kg

For the given weights the Z-value lies in the inequalities as shown

$\frac{40-40}{4} < Z < \frac{45-40}{4} = > 0 < Z < 1.25$

Now the probability distribution for this statistic is

$P(0 < Z < 1.25)=0.3944$

Hence,the number of students with their weights between 40-45kg are

$0.3944\times1000=394.4\approx394$

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