6. Records indicate that the daily high January temperatures on a tropical islan

Question

6. Records indicate that the daily high January temperatures on a tropical island tend to have a normal distribution with mean 82°F and standard deviation of 2.5°F. A tourist arrives on the island on a randomly selected day in January.

a. What is the probability that the high temperature will be 86°F?

b. What is the probability that the high temperature will be above 85°F?

c. What is the probability that the high temperature will be between 81°F and 84°F?

d. 35% of January days will have a high temperature of at least what?

e. What is the 70th percentile of daily high temperature?

Explanation / Answer

a) Xi=86, Xbar=82, s=2.5 Substitute value sin following formula and compute z score. Find areas corresponding to z score to get the required probability

z=(Xi-Xbar)/s=(86-82)/2.5=1.6, probability is :0.4452.

b) z=(85-82)/2.5=1.2 , required probability:0.1151

c) z1=(81-82)/2.5=-0.4 and z2=(84-82)/2.5=0.8, Required probability is 0.1554+0.2881=0.4435

d) z=1.04, Xbar=82, s=2.5

1.04=(Xi-82)/2.5

Xi=84.6

Related Questions

Navigate

• Browse (All)
• Browse 6
• Subjects

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