The temperature of coffee sold at the Coffee

Answered question

2022-02-28

The temperature of coffee sold at the Coffee Bean Cafe follows the normal probability distribution, with a mean of 150 degrees. The standard deviation of this distribution is 5 degrees. (a) What is the probability that the coffee temperature is between 150 degrees and 154 degrees? (b) What is the probability that the coffee temperature is more than 164 degrees?

Answer & Explanation

star233

star233

Skilled2022-03-19Added 403 answers

Here, x be the temperature of coffe sold at the coffe bean

x~Normal (μ=150,σ=50)

a)

 P(150<x<154)

=P(150-150σ<x-μσ<154-1505)

=P(05<x-μσ<45)

=P(0<z<0.8)          ...(x-μσ=z~N(0,1))

=P(z>0)-P(z>0.8)

=0.5-0.21186

=0.2881

 Probability that coffe temperature is between 150 and 154 degrees os 0.2881

b)

P(x>164)

=P(x-μσ<164-1505)

=P(z>145)          ...(x-μσ=z~N(0,1))

=P(z>2.8)

=0.002555

 Probability that coffe temperature is more than 164 degree is 0.002555

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