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g Workers employed in a large service industry have an average wage of $9.00 per hour with a standard deviation of $0.50. The industry has 64 workers of a certain ethnic group. These workers have an average wage of $8.85 per hour. Calculate the probability of obtaining a sample mean less than or equal to $8.85 per hour. (Round your answer to four decimal places.)

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JeanaShupp

Answer: 0.3821

Step-by-step explanation:

Let x be the random variable that represents the wages.

Given: Workers have an average wage of $9.00 per hour with a standard deviation of $0.50.

The probability of obtaining a sample mean less than or equal to $8.85 per hour:

[tex]P(X<8.85)=P(\dfrac{X-mean}{standard\ deviation}<\dfrac{8.85-9.00}{0.50})\\\\=P(Z<-0.3)\\\\=1-P(0.3)\\\\=1-0.6179\\\\=0.3821[/tex]

The required probability = 0.3821

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