The weight of a product is normally distributed with a mean of 4 ounces and a variance of .25 squared ounces. What is the probab
ility that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces
1 answer:
Answer: 0.0228
Step-by-step explanation:
Let x be the weight of a product.
The probability that a randomly selected unit from a recently manufactured batch weighs more than 5 ounces:
![P(X>5)\\\\=P(\dfrac{X-Mean}{\sqrt{Variance}}>\dfrac{5-4}{\sqrt{0.25}})\\\\=P(Z>\dfrac{1}{0.5}) \ \ \ [z=\dfrac{X-Mean}{\sqrt{Variance}}]\\\\=P(z>2)\\\\=1-P(Z](https://tex.z-dn.net/?f=P%28X%3E5%29%5C%5C%5C%5C%3DP%28%5Cdfrac%7BX-Mean%7D%7B%5Csqrt%7BVariance%7D%7D%3E%5Cdfrac%7B5-4%7D%7B%5Csqrt%7B0.25%7D%7D%29%5C%5C%5C%5C%3DP%28Z%3E%5Cdfrac%7B1%7D%7B0.5%7D%29%20%20%5C%20%5C%20%5C%20%5Bz%3D%5Cdfrac%7BX-Mean%7D%7B%5Csqrt%7BVariance%7D%7D%5D%5C%5C%5C%5C%3DP%28z%3E2%29%5C%5C%5C%5C%3D1-P%28Z%3C2%29%5C%5C%5C%5C%3D1-0.9772%5C%20%5C%20%20%5B%5Ctext%7BUsing%20p%20value%20table%7D%5D%5C%5C%5C%5C%3D0.0228)
Hence, the required probability = 0.0228
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