Answer in Statistics and Probability for Shilpi Mittal #122317

Question #122317

The height of the students in a certain class is following normal distribution with mean height as 165 cm and standard deviation of 25 cm. There are 60 students in that class. Determine
i. The number of students whose height is more than 158 cm.
ii. The number of students whose height is lying between 155 and 172 cm.

Expert's answer

$i) Given \; that, μ=165, σ=25, n=60, then,\\ P(x>158)=P(Z>\frac{158-165}{25})\\ =P(Z>-0.28)=0.5+P(0<Z<0.28)\\ =0.5+0.1103=0.6103\\ number\;of\;students=60\times0.6103=36.63\approx37\\ ii) P(155<x<172)\\ =P(\frac{155-165}{25})<Z<\frac{172-165}{25})\\ =P(-0.4<Z<0.28)\\ =P(0<Z<0.4)+P(0<Z<0.28)\\ =0.1554+0.1103=0.2657\\ number\;of\;students=60\times0.2657=15.94\approx16\\$

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Comments

Cel

16.10.21, 10:56

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Assignment Expert

10.05.21, 11:13

Dear helen, please use the panel for submitting a new question.

helen

05.05.21, 04:30

In a school with 500 students, the average height is 165 +-10 cm. Assuming that the height follows the normal distribution: If we choose a sample of 25 people from the above school: What is the probability that a student is taller than 169 cm? What is the probability that a student is less than 163 cm tall?