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8_murik_8 [283]
3 years ago
8

Assume that the number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100

. what is the probability that in a randomly selected hour the number of watches produced is greater than 500
Mathematics
2 answers:
horsena [70]3 years ago
8 0
To evaluate the <span>probability that in a randomly selected hour the number of watches produced is greater than 500 we proceed as follows:
z=(x-</span>μ<span>)/</span>σ
where:
x=500
μ=500
σ=100
thus
z=(500-500)/200=0

Thus:
P(x>500)=1-P(x<500)=1-P(z<0)=1-0.5=0.5

Answer: 0.5~50%
Karolina [17]3 years ago
8 0

Answer:  0.5

 

Step-by-step explanation:

Given :  The number of watches produced every hour is normally distributed with a mean of 500 and a standard deviation of 100.

i.e. \mu = 500\text{ and } \sigma= 100

Let x be the number of watches produced every hour.

Then, the probability that in a randomly selected hour the number of watches produced is greater than 500 will be :

P(x>500)=1-P(x\leq500)\\\\=1-P(\dfrac{x-\mu}{\sigma}\leq\dfrac{500-500}{100})\\\\=1-P(z\leq0)\ \ [\because\ z=\dfrac{x-\mu}{\sigma}]\\\\=1-0.5\ \ [\text{ By z-table}]\\\\=1-0.5=0.5

Hence, the probability that in a randomly selected hour the number of watches produced is greater than 500 =0.5.

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