Given a normal population whose mean is 335 and whose standa

Given a normal population whose mean is 335 and whose standard deviation is 68, find each of the following:

A. The probability that a random sample of 4 has a mean between 343 and 357.

Probability =

B. The probability that a random sample of 19 has a mean between 343 and 357.

Probability =

C. The probability that a random sample of 30 has a mean between 343 and 357.

Probability =

Solution

A. The probability that a random sample of 4 has a mean between 343 and 357.

Probability = P(343<xbar<357)

= P((343-335)/(68/sqrt(4)) <(xbar-mean)/(s/vn) <(357-335)/(68/sqrt(4)))

=P(0.24<Z<0.65) =0.1473 (from standard normal table)

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B. The probability that a random sample of 19 has a mean between 343 and 357.

Probability = P(343<xbar<357)

= P((343-335)/(68/sqrt(19)) <(xbar-mean)/(s/vn) <(357-335)/(68/sqrt(19)))

=P(0.51<Z<1.41) =0.2258 (from standard normal table)

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C. The probability that a random sample of 30 has a mean between 343 and 357.

Probability = P(343<xbar<357)

= P((343-335)/(68/sqrt(30)) <(xbar-mean)/(s/vn) <(357-335)/(68/sqrt(30)))

=P(0.64<Z<1.77) =0.2227 (from standard normal table)