Question

Suppose the number of items you can deliver in a day is a random variable with some unknown distribution with a mean = 35 and a standard deviation of 8. What is the probability a random sample of 36 days would have a mean between 32.6 and 34.6?

Answer 1

Answer:

P = 0.3462

Step-by-step explanation:

See attached photo for work.

We have a sample mean of 35, a sample standard deviation of 8, and a sample size of 36.  

You need to see that the probability of the number of items you can deliver in a day is between 32.6 and 34.6.

The answer is 0.3462, so there's about a 34.62% chance that you will deliver an average of 32.6 to 34.6 packages per day.

Answer 2

The probability a random sample of 36 days would have a mean between 32.6 and 34.6 is 0.3462

What is probability?

• The chance of happening of an event is called probability.
• Probability is always less then 1

What is mean?

Mean is actually the average of all the observations.

What is standard deviation?

A standard deviation (or σ) is a measure of how dispersed the data is in relation to the mean

What is z-score?

A z-score is a numerical measurement that describes a value's relationship to the mean of a group of values.

How to find the probability of the random sample?

According to the problem,

• Mean = 35
• Standard Deviation = 8
• Sample = 36

Here we need to find  P(32.6 < x < 34.6)

• Firstly we should find the z-score of 32.6 and 34.6

$z_{32.6}$ = $\frac{32.6-35}{\frac{8}{\sqrt{36} } }$ = - 1.80

$z_{34.6} = \frac{34.6-35}{\frac{8}{\sqrt{36} } }$ = -0.30

∴ P(32.6 < x < 34.6) = P ( -1.80 < z < -0.30)

= P(z< -0.30) - P(z < -1.80)

= 0.3821 - 0.0359 = 0.3462

∴  The required probability is 0.3462

Find out more about "Probability" here : https://brainly.com/question/24756209

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