Evaluate the following 1. \( 5 \mathrm{P5} \) 2. \( 8 \mathrm{P4} \) 3. 10 PP 4. 7 P 2 5. 12 P 3

A high-yield string bean plant will produce, on average, at least 30 beans per week. Of 639 bean plants in a greenhouse, 426 plants produced less than 30 beans per week. What is the approximate probability that a randomly selected string bean plant will be a high-yield plant?

Between 12:00 PM and 1:00 PM, cars arrive at a local bank's drive-thru at the rate of 8 cars per hour ( 0.13 car per minute). The formula below from probability can be used to determine the probability that a car will arrive within t minutes of 12:00 PM. Use this information to answer the questions given below in parts (a)-(e). F(t) \( =1-e^{-0.13 t} \) (a) What is the probability that a car will arrive within 35 minutes of \( 12: 00 \) PM (that is, before 12:35 PM)? \( \mathrm{F}(35)=0.989 \) (Round to three decimal places as needed.) (b) What is the probability that a car will arrive within 40 minutes of \( 12: 00 \) PM (that is, before 12:40 PM)? F(40) \( =\square \) (Round to three decimal places as needed.)

Major Hurricanes A major hurricane is a hurricane with wind speeds of 111 miles per hour or greater. During the 20th century, the mean number of major hurricanes to strike the U.S. mainland per year was about 0.6 . Find the probability that in a given year (a) exactly one major hurricane strikes the U.S. mainland, (b) at most one major hurricane strikes the U.S. mainland, and (c) more than one major hurricane strikes the U.S. mainland. (Source:

Between 12:00 PM and 1:00 PM, cars arrive at a bank's drive-thru at the rate of 18 cars per hour ( 0.3 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within \( t \) minutes of 12:00 PM. Complete parts (a)-(c). F(t) \( =1-e^{-0.3 t} \) (a) Determine how many minutes are needed for the probability to reach 30\%. About \( \square \) minutes are needed for the probability to reach 30\%. (Round to two decimal places as needed.)

Between 12:00 PM and 1:00 PM, cars arrive at a bank's drive-thru at the rate of 18 cars per hour (0.3 car per minute). The following formula from statistics can be used to determine the probability that a car will arrive within \( t \) minutes of \( 12: 00 \) PM. Complete parts (a)-(c). \[ F(t)=1-e^{-0.3 t} \] (a) Determine how many minutes are needed for the probability to reach \( 30 \% \). About 1.19 minutes are needed for the probability to reach \( 30 \% \). (Round to two decimal places as needed.) (b) Determine how many minutes are needed for the probability to reach \( 90 \% \). About \( \square \) minutes are needed for the probability to reach \( 90 \% \). (Round to two decimal places as needed.)