Answered

At Westonci.ca, we make it easy to get the answers you need from a community of informed and experienced contributors. Discover comprehensive solutions to your questions from a wide network of experts on our user-friendly platform. Our platform provides a seamless experience for finding reliable answers from a network of experienced professionals.

X is normally distributed with a mean of 100 and a standard deviation of 15. What is the probability of randomly sampling a score from X and having it be greater than or equal to 126 ​

Sagot :

DragonPup315

Answer:

Using calculator: 0.0415

Using Z-score Table: 0.0418

Step-by-step explanation:

There are two ways you can solve this problem.

1. Use the normal distribution function on a calculator.

Entered values:

Lower Limit: 126

Upper Limit: 999999999999999... (To encompass all the data)

Standard Deviation: 15

Mean: 100

2. Find the Z score and look up probabilities on table.

Formula for Z score:

[tex]Z=\frac{x-mean}{standard deviation} \\\\Z= \frac{126-100}{15}=1.7333...[/tex]

Z = 1.7333

This means that the value 126 is 1.733 standard deviations away from the mean. We can look this value up on the Z table to find its corresponding probability.

This will show us the probability of the random sampling being equal to or lower than 126.

P = 0.9582

So to find the probability of it being above, we simply just calculate the inverse as all probabilities on the curve = 1.

1-0.9582 = 0.0418

NOTE: Values found from the table will usually be a bit different from if you find it from a calculator, the one you need will depend on the method you use in class.

Hope this helped!

We appreciate your time. Please revisit us for more reliable answers to any questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. We're here to help at Westonci.ca. Keep visiting for the best answers to your questions.