5.94 When fishing off the shores of Florida, a spotted sea trout must be between

Question

5.94 When fishing off the shores of Florida, a spotted sea trout must be between 14 and 24 inches long before it can be kept; otherwise, it must be returned to the waters. In a region of the Gulf of Mexico, the lengths of spotted sea trout that are caught are normally distributed with a mean of 22 inches and a standard deviation of 4 inches. Assume that each spotted sea trout is equally likely to be caught by a fisherman. a What is the probability that a fisherman catches a spotted sea trout within the legal limits? b The fisherman caught a large spotted sea trout. He wants to know whether the length is in the top 5% of the lengths of spotted sea trout in that region. Find the length x for which only 5% of the spotted sea trout in this region wil be larger than x. c What is the probability that the fisherman will catch three trout outside the legal limits before catching his first legal spotted sea trout (between 14 and 24 inches)?

Explanation / Answer

a) probability =P(14<X<24)=P((14-22)/4<Z<(24-22)/4) =P(-2<Z<0.5)=0.6915-0.0228 =0.6687

b) for top 5% ; at 95th percentile ; zscore =1.6449

threfore x =mean +z*Std deviaiton =28.58

c)

probability of catching 3 trout outside legal limits and then one with in limit =(1-0.6687)3*0.6687=0.0243

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.