The weight of toys a toddler owns has a population mean of 15.8kg and a population standard deviation of 4.2kg. then the probability a toy store owner could select a sample of 49 toddlers and find the sample mean to be 15.1kg or less is 0.121 and 15.1kg or more is 0.879.
Given Information:
Population mean, μ = 15.8 kg
Population standard deviation, σ = 4.2 kg
For finding the probability for the sample mean, we first need to find the standard score.
(a) For sample mean to be 15.1kg or less,
z = (x - μ) / (σ/√n)
Here, x = 15.1
⇒ z = (15.1 - 15.8) / (4.2/√49
z =-0.7 / (4.2/7)
z = -1.17
Now, we can use the z-table to find the probability of the sample mean to be 15.1kg or less.
∴ P(x ≤ 15.1) = 0.121
(b) Now, to find the probability of sample mean to be 15.1kg or more, we can simply subtract P(x ≤ 15.1) from 1.
⇒ P(x ≥ 15.1) = 1 - P(x ≤ 15.1)
P(x ≥ 15.1) = 1 - 0.121
P(x ≥ 15.1) = 0.879
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