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.   1) limn→∞P((n/3)−10≤Sn≤(n/3)+10)=   2) limn→∞P(n/3−n/6≤Sn≤n/3+n/6)=   3)limn→∞P(n/3− sqrt2n/5≤Sn≤n/3+sqrt2n/5)=

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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.

 

1) limn→∞P((n/3)−10≤Sn≤(n/3)+10)=

 

2) limn→∞P(n/3−n/6≤Sn≤n/3+n/6)=

 

3)limn→∞P(n/3− sqrt2n/5≤Sn≤n/3+sqrt2n/5)=

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