Find the limits

Question

Let Sn be the number of successes in n independent Bernoulli trials, where the probability of success at each trial is 1/3. Provide a numerical value, to a precision of 3 decimal places, for each of the following limits. You may want to refer to the standard normal table.

Normal Table

1) limn→∞P(n/3 − 10 ≤ Sn ≤ n/3 + 10)=
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2) limn→∞P(n/3 − n/6 ≤ Sn ≤ n/3 + n/6)=
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3)limn→∞P(n/3 − √2n/5 ≤ Sn ≤ n/3 + √2n/5)=
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Answer 1

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