We have to find the probability that the mean of the weights of the selected at random 10 goats exceeds 65 kg.
We have a normal distribution,
"\u03bc=60,\u03c3=10,n=10."
Let's convert it to the standard normal distribution,
"\\bar{z}=\\cfrac{\\bar{x}-\\mu}{\\sigma\/\\sqrt{n}},\\\\\n\\bar{z}=\\cfrac{65-60}{10\/\\sqrt{10}}=1.58,\\\\\nP(\\bar{X}>65)=P(\\bar{Z}>1.58)=\\\\\n=1-P(\\bar{Z}<1.58)=\\\\\n=1-0.9429=0.0571\\text{ (from z-table).}"
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