Use the normal distribution of fish lengths for which the mean is 9 inches and t

Question

Use the normal distribution of fish lengths for which the mean is 9 inches and the standard deviation is 2 inches. Assume the variable x is normally distributed. (a) What percent of the fish are longer than 11 inches? (b) If 500 fish are randomly selected, about how many would you expect to be shorter than 8 inches? (a) Approximately __% of fish are longer than 11 inches. (Round to two decimal places as needed.) (b) You would expect approximately __ fish to be shorter than 8 inches. (Round to the nearest fish.)

Explanation / Answer

a) P(X > 11)

= P(z > (11 - 9)/2)

= P(z > 1)

= 0.1587

Hence,

The percentage is 15.87%

b) P(X < 8)

= P(z < (8 - 9)/2)

= P(z < -0.5)

= 0.3085

Hence,

Expected number of fish shorter than 8 inches = 0.3085*500 = 154

Related Questions

Navigate

• Browse (All)
• Browse U
• Subjects

---

---

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