Question

Every day Cara runs for five miles. Suppose that the time it takes her to complete...

Every day Cara runs for five miles. Suppose that the time it takes her to complete the run is a random variable that is normally distributed with a mean of 50 minutes and a standard deviation of 5 minutes. Today Cara ran the five miles in 46 minutes. What is the probability that she will beat her time tomorrow?

Math   Statistics-And-Probability   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

Cara beat her time tomorrow means she run faster than today.

That is time taken by her to complete five miles is less than 46 min

Given,

= 50 , = 5

We convert this to standard normal as

P( X < x) = P( Z < x - / )

So,

P( X < 46) = P( Z < 46 - 50 / 5)

= P( Z < -0.8)

= 1 - P( Z < 0.8)

= 1 - 0.7881 (Probability calculated from Z table)

= 0.2119

0 0
Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
You run 3 miles every day. On a given day, you record the time it takes...
You run 3 miles every day. On a given day, you record the time it takes you (in minutes), and this takes values 25, ..., 31, with each one being equally likely. The time it takes you on any day is independent of the time on other days. You used to record your time every day. Now, you just remember how long it took you every day, and then at the end of the week, record your best time from...
Let x denote the time it takes to run a road race. Suppose x is approximately...
Let x denote the time it takes to run a road race. Suppose x is approximately normally distributed with a mean of 190 minutes and a standard deviation of 21 minutes. If one runner is selected at random, what is the probability that this runner will complete this road race in less than 205 minutes? Round your answer to four decimal places. P= #2 Let x denote the time it takes to run a road race. Suppose x is approximately...
Mrs Smith walks to work every day. If she takes the most direct route, her journey...
Mrs Smith walks to work every day. If she takes the most direct route, her journey time is 10 minutes. However, this route follows a busy main road and, if it has been raining, she often gets splashed by traffic driving through puddles. Before she leaves for work therefore, she checks the weather: if the sky is no more than 40% covered by cloud, she takes the most direct route, but otherwise she takes a longer route where she is...
Suppose that the time it takes to complete a Ph.D. in mathematics is normally distributed with...
Suppose that the time it takes to complete a Ph.D. in mathematics is normally distributed with a mean of 5.8 years and a standard deviation of 0.7 years. Find the probability that a random sample of 15 mathematicians has an average time to completion of under 5.5 years. (round to three decimal places)
The time it takes students to complete a quiz is Normally distributed with a mean of...
The time it takes students to complete a quiz is Normally distributed with a mean of 45 minutes and a standard deviation of 4 minutes.   a)What percent of all students take longer than 50 minutes to complete the quiz? Round your answer to the nearest whole percent. Don't write the percent symbol in your answer. b)If you take a sample of 30 students, what is the probability that the average amount of time needed to complete the quiz for this...
The average time it takes a group of students to complete a certain assignment is 36...
The average time it takes a group of students to complete a certain assignment is 36 minutes. The standard deviation is 4 minutes. Assume the variable is normally distributed. Now find the probability that if a group of 9 randomly selected students complete the assignment, the mean time it takes the group will complete the assignment in less than 33 minutes. Include drawings in your work. Use Traditional Method for hypothesis testing unless specified otherwise. Use correct rounding rule for...
A UJ student drives every day from his home to his university. Time to reach university...
A UJ student drives every day from his home to his university. Time to reach university is distributed normally with a mean of 50 minutes and with standard deviation of 12 minutes. Find the probability that the time to reach university will take between 27.08 and 52.40 minutes?
7) The time it takes college freshman to complete the Mason Basic Reasoning Test is normally...
7) The time it takes college freshman to complete the Mason Basic Reasoning Test is normally distributed with a mean of 24.6 minutes with a standard deviation of 5.8 minutes. a) What is the probability that a college freshman will take more than 35 minutes to complete the exam? b) What is the probability that a student will take less than 20 minutes to complete the exam?
A) The amount of time it takes students to complete a quiz is uniformly distributed between...
A) The amount of time it takes students to complete a quiz is uniformly distributed between 35 to 65 minutes. One student is selected at random. Find the following events: a. The probability density function (pdf) of amount of time taken for the quiz. b. The probability that the student requires more than 50 minutes to complete the quiz.(1 mark) c. The probability that completed quiz time is between 45 and 55 minutes. (1 mark) d. The probability that the...
9.   Suppose that the time that it takes a student to complete this test is normally...
9.   Suppose that the time that it takes a student to complete this test is normally distributed. The mean time is 58 minutes with a standard deviation of 11 minutes. Use the empirical rule to solve the following questions. Answers using the normal calculator and not the empirical rule will be marked as wrong. a.   What is the probability that a person will take between 47 and 58 minutes? (Draw a picture to show your answer.) b.   What is the...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT