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Let’s check out your problem:

(b) P( bar(x) < 66.4)=0.7639 (Round to four decimal places as needed.) (c) P( bar(x) >= 64.2)= ◻ (Round to four decimal places as needed.)

(b) P(xˉ<66.4)=0.7639 P(\bar{x}<66.4)=0.7639 (Round to four decimal places as needed.)\newline(c) P(xˉ≥64.2)= P(\bar{x} \geq 64.2)= □ \square (Round to four decimal places as needed.)

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Full solution

Q. (b) P(xˉ<66.4)=0.7639 P(\bar{x}<66.4)=0.7639 (Round to four decimal places as needed.)\newline(c) P(xˉ≥64.2)= P(\bar{x} \geq 64.2)= □ \square (Round to four decimal places as needed.)
  1. Identify complement: Identify the complement of the event given in part (b) to find the probability for part (c). Since P(xˉ<66.4)=0.7639P( \bar{x} < 66.4) = 0.7639, the complement is P(xˉ≥66.4)=1−0.7639P( \bar{x} \geq 66.4) = 1 - 0.7639.
  2. Calculate complement probability: Calculate the complement probability: 1−0.7639=0.23611 - 0.7639 = 0.2361. This is the probability that the sample mean is greater than or equal to 66.466.4.
  3. Compare probabilities: Since 64.264.2 is less than 66.466.4, the probability that xˉ≥64.2\bar{x} \geq 64.2 will be higher than 0.23610.2361. However, without additional information or a distribution table, we cannot calculate the exact value for P(xˉ≥64.2)P( \bar{x} \geq 64.2).

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