Answered

Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Connect with professionals ready to provide precise answers to your questions on our comprehensive Q&A platform. Discover in-depth answers to your questions from a wide network of professionals on our user-friendly Q&A platform.

Suppose the salaries of university professors are approximately normally distributed with a mean of $65,000 and a standard deviation of $7,000. If a random sample of size 25 is taken and the mean is calculated, what is the probability that the mean value will be between $62,500 and $64,000? a. .1465 b. .0827 c. .0371 d. .2005

Sagot :

fichoh

Answer:

0.2005

Step-by-step explanation:

Mean, m = 65000

Standard deviation, σ= 7000

Sample size, n = 25

Let X = random variable of salary

Recall:

Z = (μ - x) /(σ/√n)

P(62500 ≤ x ≤ 64000) =?

Pr((65000 - 62500)/7000/√25 ≤ z ≤ (65000 - 64000) / 7000/√25)

P(2500 / 1400 ≤ z ≤ 1000/1400)

P = (1.79 ≤ z ≤ 0.714)

Using the normal distribution table or a Z probability calculator

0.4633 - 0.2624

= 0.2009

We hope our answers were helpful. Return anytime for more information and answers to any other questions you may have. We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.