Question

The length of time it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of 5 minutes and a standard deviation of 2 minutes. Find the probability that it takes at least 8 minutes to find a parking space. (Round your answer to four decimal places.)

Answer 1

Answer: 0.0668

Step-by-step explanation:

Given: Mean : $\mu = 5\text{ minutes}$

Standard deviation : $\sigma = 2\text{ minutes}$

The formula to calculate z is given by :-

$z=\dfrac{X-\mu}{\sigma}$

To check the probability it takes at least 8 minutes (X≥ 8) to find a parking space.

Put X= 8 minutes

$z=\dfrac{8-5}{2}=1.5$

The P Value =$P(z\geq1.5)=1-P(z\leq1.5)=1- 0.9331927=0.0668073\approx0.0668$

Hence, the probability that it takes at least 8 minutes to find a parking space = 0.0668

Answer 2

The probability that it takes atleast 8 minutes to find a parking space is 0.0668

Given the Parameters :

• Mean = 5 minutes
• Standard deviation = 2 minutes
• X ≥ 8

First we find the Zscore :

• Zscore = (X - mean) / standard deviation

Zscore = (8 - 5) / 2 = 1.5

The probability of taking atleast 8 minutes can be expressed thus and calculated using the normal distribution table :

P(Z ≥ 1.5) = 1 - P(Z ≤ 1.5)

P(Z ≥ 1.5) = 1 - 0.9332

P(Z ≥ 1.5) = 0.0668

Therefore, the probability, P(Z ≥ 1.5) is 0.0668

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