Answer to Question #163814 in Statistics and Probability for Zafar

Question #163814

Cut fruit is packed for sale in a supermarket. The weights of packages are normally distributed with a mean of 201.49 grams and variance of 24.63 grams.

Given that 5% of the distribution lies below the Z value of -1.64485, find the package weight that has 5% of the distribution above it. Give your result correct to four decimal places.


1
Expert's answer
2021-02-24T06:58:15-0500

Given P(Z<1.64485)=0.05.P(Z<-1.64485)=0.05. Then P(Z>1.64485)=0.05.P(Z>1.64485)=0.05.


Z=XμσZ=\dfrac{X-\mu}{\sigma}

Given μ=201.49 g,σ=24.63 g.\mu=201.49\ g, \sigma=24.63\ g.

Then


X201.4924.63=1.64489\dfrac{X-201.49}{24.63}=1.64489

X=1.64489(24.63)+201.49242.0036X=1.64489(24.63)+201.49\approx242.0036

242.0036242.0036 grams.



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