Question #349792

The weights(kg) of 11 stem B follow a normal distribution and has a mean of 50 and a standard deviation of 5 how many students have weights greater than 57?

1
Expert's answer
2022-06-13T12:02:59-0400

We have a normal distribution with μ=50,\mu=50, σ=5.\sigma=5.

Let's find the corresponding z-score for X=57X=57 :

z=Xμσ=57505=1.4z=\frac{X-\mu}{\sigma}=\frac{57-50}{5}=1.4


So,

P(X>57)=P(z>1.4)=1P(z<1.4)=10.9192=0.0808.P(X>57)=P(z>1.4)=1-P(z<1.4)=1-0.9192=0.0808.


As the total number of students is 11 and the probability to have weight greater than 57 is 0.0808,

the number of students of such weight equals:

110.0808=0.88881.11\cdot 0.0808=0.8888\approx1.


Answer: The number of students that have weights greater than 57 is 1.\approx1.


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