Answer:
0.3341 is the probability that a randomly selected time interval between eruptions is longer than 103 minutes.
Step-by-step explanation:
We are given the following information in the question:
Mean, μ = 91 minutes
Standard Deviation, σ = 28 minutes
We are given that the distribution of time between the eruptions is a bell shaped distribution that is a normal distribution.
Formula:
[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]
a) P( time interval between eruptions is longer than 103 minutes)
P(x > 103)
[tex]P( x > 103) = P( z > \displaystyle\frac{103 - 91}{28}) = P(z > 0.4286)[/tex]
[tex]= 1 - P(z \leq 0.4286)[/tex]
Calculation the value from standard normal z table, we have,
[tex]P(x >103) = 1 - 0.6659 = 0.3341 = 33.41\%[/tex]
0.3341 is the probability that a randomly selected time interval between eruptions is longer than 103 minutes.
