Acme Confectionery has launched a new bar called Chocolate Crunch - Leaving Cert Mathematics - Question 8 (i) - 2018
Question 8 (i)
Acme Confectionery has launched a new bar called Chocolate Crunch. The weights of these new bars are normally distributed with a mean of 4-64 g and a standard deviat... show full transcript
Worked Solution & Example Answer:Acme Confectionery has launched a new bar called Chocolate Crunch - Leaving Cert Mathematics - Question 8 (i) - 2018
Step 1
Calculate $z_1$ for 4-6 g
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Answer
To find z1, we use the formula:
z1=σ/nX−μ
Where:
X=4.6 g,
μ=4.64 g,
σ=0.12 g,
n=10.
Substituting, we get:
z1=0.12/104.6−4.64=0.0379−0.04≈−1.05409.
Step 2
Calculate $z_2$ for 4-7 g
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Answer
For z2, we apply the same formula:
z2=σ/nX−μ
Where:
X=4.7 g.
Substituting, we get:
z2=0.12/104.7−4.64=0.03790.06≈1.581138.
Step 3
Find the probability $p(-1.05 < z < 1.58)$
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Answer
We can find the probability by using the standard normal distribution table:
From the Z-table, P(Z<1.58)≈0.9429 and P(Z<−1.05)≈0.1487.
