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Nataliya [291]
2 years ago
8

Assume that the readings at freezing on a batch of thermometers are Normally distributed with mean 0°C and standard deviation 1.

00°C. Find P_{60}, the 60-percentile of the distribution of temperature readings. This is the temperature reading separating the bottom 60% from the top 40%.
Mathematics
1 answer:
andre [41]2 years ago
8 0

Answer:

P_{60} = 0.254    

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 0

Standard Deviation, σ = 1.00

We are given that the distribution of readings at freezing on a batch of thermometers is a bell shaped distribution that is a normal distribution.

Formula:

z_{score} = \displaystyle\frac{x-\mu}{\sigma}

We have to find P_{60}

P(X<x) = 0.0600

We have to find the value of x such that the probability is 0.600

P(X < x)  

P( X < x) = P( z < \displaystyle\frac{x - 0}{1})=0.600  

Calculation the value from standard normal z table, we have,  

\displaystyle\frac{x - 0}{1} = 0.254\\x = 0.254

\bold{P_{60} = 0.254}

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