\(X\sim N(50,100)\). Find:
Question 2
The heights of students in a school are normally distributed with mean 165 cm and standard deviation 8 cm.
(a)Find the probability that a randomly chosen student is taller than 177 cm.
(b)In a group of 200 students, how many would you expect to be between 157 and 173 cm?
(a)
\(Z= frac{177-165}{8}=1.5\)
\(P(Z>1.5)=1-0.9332\)
(b)
\(Z=\pm1\)
\(P(-1
Answer
Approx \(137\) students
Question 3
If \(X\sim N(\mu,\sigma^2)\) and \(P(X<70)=0.8413\) and \(P(X<50)=0.1587\), find \(\mu\) and \(\sigma\).
Recognise probabilities
\(P(Z<1)=0.8413\Rightarrow frac{70-\mu}{\sigma}=1\); \(P(Z<-1)=0.1587\Rightarrow frac{50-\mu}{\sigma}=-1\)
SolveAdding: \( frac{120-2\mu}{\sigma}=0\Rightarrow\mu=60\); \(\sigma=10\)
Answer
\(\mu=60,\;\sigma=10\)
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