A population of values has a normal distribution with μ=68.1andσ=20.7.

(a) Find the probability that a single randomly selected value is less than 78.8. Round your answer to four decimal places.

(b) Find the probability that a randomly selected sample of size n = 38 has a mean less than 78.8. Round your answer to four decimal places.

Answer :

Given :

The population mean (μ)=68.1

The population standard deviation (σ)=20.7

Solution :

(a) The probability that a single randomly selected value is less than 78.8 :

P(x<78.8)=P(xμσ<78.868.120.7) =P(z<0.517) =0.6974

(b) The probability that a randomly selected sample of size n=38 has a mean less than 78.8 :

P(x¯<78.8)=P(x¯μσn<78.868.120.738) =P(z<3.186) =0.9993

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