Find Probability of Item Weight in Normal Distribution | Statistics Help

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To find the probability of item weights between 8 and 16 ounces in a normal distribution with a mean of 12 and a standard deviation of 2, the Z-scores are calculated as Z=(X-μ)/σ. For the upper limit of 16 ounces, Z equals 2, leading to a cumulative probability of approximately 0.9772. For the lower limit of 8 ounces, Z equals -2, giving a cumulative probability of about 0.0228. The probability that an item weighs between 8 and 16 ounces is then found by subtracting these probabilities, resulting in approximately 0.9544. This indicates that about 95.44% of items fall within the specified weight range.
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need help with this problem
x~normal(mean= 12, stdev=2)
item weight from 8 to 16 ounces
i have a random sample of 7 items and need to find the probability that 3 of those items fulfill the weight
each item is independent

this is what i got at the moment
z=(16-12)/(2) = 2
p(z<2)-p(z<-2)
=.9772-.0228
=.9544
 
Last edited:
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You need to use the transformation Z=(X-μ)/σ, and then read the range off of your table.

(σ = std.dev, and μ=mean)
 
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