Suppose that the actual weight of 64-ouncebags of sugarhave a skewed distribution witha mean of 65.0ounces anda standard deviation of 0.5. Weights will be measured for a random sampleof 32bags and the sample mean will be computed.(1)What distributionwill be sample mean have in this setting?(a)Exact normaldistribution (b)Approximate t distribution(c)Approximatenormal distribution(d)Standard normaldistribution(2)What is the probabilitythat the sample mean weight of the 32 bags of sugar is between 64.9 ounces and 65.2 ounces?
(b)Approximate t distribution
\\Mean (\mu)= 65 \\Standard\;Deviation (\sigma)= 0.5
Sample size (n) = 32
Since we know that
P(64.9 < x < 65.2)=?
This implies that
P(64.9 < x < 65.2) = P(-1.1312 < z < 2.2624) = P(Z < 2.2624) - P(Z < -1.1312)
P(64.9 < x < 65.2) = 0.9881636495316076 - 0.12898546097486252
PS: you have to refer z score table to find the final probabilities.
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