Magdalena Norton

2022-05-01

Without assuming that the diameters of apple pies are distributed according to the normal distributions, estimated the probability that the mean diameter is larger than 32 cm. The sample standard deviation is estimated to be 2. The sample mean is 28 and the sample size is 100.

When I used CLT (because the sample size is >30). I am getting a z score of 20? Is this correct?

When I used CLT (because the sample size is >30). I am getting a z score of 20? Is this correct?

Ann Mathis

Beginner2022-05-02Added 11 answers

Central Limit Theorem indicates that: For samples of size n taken from a population with mean, $\mu $, and a standard deviation, $\sigma $,

${\mu}_{\overline{x}}=\mu ,{\sigma}_{\overline{x}}=\frac{\sigma}{\sqrt{n}}$

This problem is actually a reversed form of CLT. We are told the sample mean and standard deviation, and we need to compute the population mean and standard deviation.

${\sigma}_{\overline{x}}=2=\frac{\sigma}{\sqrt{100}},\sigma =20$

$\mu ={\mu}_{\overline{x}}=28$

Thus it will just be $P(Z>\frac{32-28}{20})=P(Z>0.2)=1-P(Z<0.2)$

${\mu}_{\overline{x}}=\mu ,{\sigma}_{\overline{x}}=\frac{\sigma}{\sqrt{n}}$

This problem is actually a reversed form of CLT. We are told the sample mean and standard deviation, and we need to compute the population mean and standard deviation.

${\sigma}_{\overline{x}}=2=\frac{\sigma}{\sqrt{100}},\sigma =20$

$\mu ={\mu}_{\overline{x}}=28$

Thus it will just be $P(Z>\frac{32-28}{20})=P(Z>0.2)=1-P(Z<0.2)$

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