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The distribution of the weights of loaves of bread from a certain bakery follows approximately a normal distribution. Based on a very large sample, it was found that 10 percent of the loaves weighed less than 15.34 ounces, and 20 percent of the loaves weighed more than 16.31 ounces. What are the mean and standard deviation of the distribution of the weights of the loaves of bread?

Respuesta :

Answer: Mean would be  0.455 and standard deviation would be 15.926.

Step-by-step explanation:

Since we have given that

P(Z>z)=20%

So, 1-P(Z≤z)=0.2

P(Z≤z)=1-0.2=0.8

Using the normal table, we get that

z = 0.845

[tex]\dfrac{\bar{x}-\mu}{\sigma}\\\\\dfrac{16.31-\mu}\sigma}=0.845\\\\16.31-\mu=0.845\times \sigma----------------(1)[/tex]

Now, P(Z≤z) = 10%= 0.10

So, z = -1.28

[tex]\dfrac{\bar{x}-\mu}{\sigma}=-1.28\\\\\dfrac{15.34-\mu}{\sigma}=-1.28\\\\15.34-\mu=-1.28\sigma----------(2)[/tex]

From, eq(1) and (2), we get that

μ = 0.455 and σ = 15.926.

Hence, mean would be  0.455 and standard deviation would be 15.926.

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