Question

95% of students at school weigh between 62 kg and 90 kg. Assuming this data is normally distributed, what are the mean and standard deviation?

Answer 1

Answer:

Mean is 76 and standard deviation is 7.

Step-by-step explanation:

Let $\mu$ be the mean and $\sigma$ is the standard deviation of the given data,

Thus, 95% of the data lies between $\mu-2\sigma$ and $\mu+2\sigma$

Now, 95% of students at school weigh between 62 kg and 90 kg,

So, the mean is,

$\mu=\frac{62+90}{2}=\frac{152}{2}=76$

$\implies 76+2\sigma = 90$

$2\sigma = 14$

$\implies \sigma = 7$

Answer 2

We can calculate (62 + 90) / 2 = 76. it's known that 95% lies between the mean and twice the standard deviation. if the mean is "μ" and the standard deviation is "σ": μ-2σ and μ+2σ. if μ=76, then 76+2σ = 90, so 2σ = 14, so σ = 7.

the mean is 76 and the standard deviation 7.