Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0.25
0.250, point, 25 probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine
5
55 times.
Assuming that each trip is equally likely to travel before Isabella was born, what is the probability that at least one trip will travel before Isabella was born?
Round your answer to the nearest hundredth.

the probability that at least one trip will travel before Isabella was born is 0.7627

Step-by-step explanation:

Here we have , Isabella built a time travel machine, but she can't control the destination of her trip. Each time she uses the machine she has a 0.25 point, probability of traveling to a time before she was born. During the first year of testing, Isabella uses her machine 5 times. Assuming that each trip is equally likely to travel before Isabella was born, We need to find what is the probability that at least one trip will travel before Isabella was born . Let's find out:

Isabella have probability of traveling to a time before she was born of 0.25

Probability of not travelling any time before Isabella was born , given that time machine is used 5 times   :

⇒

⇒

⇒

Probability that at least one trip will travel before Isabella was born is equivalent to  1 - Probability of not travelling any time before Isabella was born i.e.

⇒

⇒

Therefore , the probability that at least one trip will travel before Isabella was born is 0.7627

hello,

b) 62.47% of the students are between 14 and 18 years old.

step-by-step explanation:

mean = 15 and standard deviation = 2

student between 14 to 18

formula used z-score

for age 14 , z score

using z-table , p(z> -0.5)=0.3085

for age 18 , z score

using z-table , p(z< 1.5)=0.9332

p(-0.5< z< 1.5)=0.9332-0.3085 = 0.6247

thus, 62.47% of the students are between 14 and 18 years old.

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