Question

In: Statistics and Probability

From past experience it is known that 90% of one-year old children can distinguish their mother’s...

  1. From past experience it is known that 90% of one-year old children can distinguish their mother’s voice from the voice of a similar sounding female. A random sample of 50 one-year olds is given this voice recognition test.
    1. Find the probability that exactly 3 children do not recognize their mother’s voice. (2 points)
    1. Find the probability that 3 or fewer children do not recognize their mother’s voice. (2 points)
    1. What is the probability that at least 47 children recognize their mother’s voice?(2 points)
    1. Find the probability that exactly 90% of the 50 children do recognize their mother’s voice. (2 points)
    1. What is the probability that exactly 49 of the 50 children recognize their mother’s voice? (2 points)
    1. Find the probability all 50 children recognize their mother’s voice. (2 points)
    1. Let the random variable x denote the number of children who recognize their mother’s voice. Find the mean of x. (2 points)
    1. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the mean of x. (2 points)
    2. Let the random variable x denote the number of children who do not recognize their mother’s voice. Find the variance of x. (2 points)

Solutions

Expert Solution

Here from the explaination given in the question it can be observed that binomial distribution can be used to find the probabilities where

and   

where P is probability that a one year old child can distinguish his/her mother's voice correctly.

n=50

a) To find probability that 3 children does not recognise there mother's voice correctly that is 47 identify it correctly.

so probability is

b) probability that 3 or fewer children does not recognise voice correctly is equal to 47,48,49,50 children answer it correctly, so probability is

This is equal to =

Hence probability is 0.250292

c) To find probability that atleast 47 children recognise their mother's voice is equal to sum of probabilites for 47,48,49,50 children who recognised their mother's voice correctly

This is same as part b because 3 or fewer children not recognising their mother's voice is equal to 47,48,49,50 recognising it correctly.

Hence answer is 0.250292

d) Firstly 90% of 50 is 45, so to find probability that exactly 45 children recognised voice correctly is given by

Hence probability is 0.1849246


Related Solutions

Assume the weights of 10 year old children are normally distributed with a mean of 90...
Assume the weights of 10 year old children are normally distributed with a mean of 90 pounds and a variance of 36. a. What is the standard deviation of the sampling mean for a sample of size 100? b. What is the 95% confidence interval for this distribution? c. What is the 99% confidence interval for this distribution? A random sample of 225 statistics tutoring sessions was selected and the number of students absent at each session was recorded. The...
Case: Rollie Hendrix is a 35-year-old husband and father of three children. Over the past six...
Case: Rollie Hendrix is a 35-year-old husband and father of three children. Over the past six months he has experienced headaches and palpitations of increasing frequency and severity. In addition, he has periods of intense anxiety and panic attacks. His wife Arlene has noticed that Rollie’s face is often pale and that he sweats more. Upon examination by his physician, Rollie was found to be severely hypertensive and in atrial fibrillation. Rollie’s physician suspected that he might have a Pheochromocytoma...
3. A What was the real rate of return over the past year (from one year...
3. A What was the real rate of return over the past year (from one year ago to today) for a stock if the inflation rate over the past year was 4.57 percent, the risk-free return over the past year was 6.99 percent, the stock is currently priced at 78.89 dollars, the stock was priced at 71.24 dollars 1 year ago, and the stock just paid a dividend of 2.47 dollars? Answer as a rate in decimal format so that...
4. From past experience, the owner of a restaurant knows that, on average, 5% of the...
4. From past experience, the owner of a restaurant knows that, on average, 5% of the groups that make reservations never show, and 7% of the groups that make reservations show up late (the other 88% percent show up on time). a) How many reservations can the owner accept and still be at least 80% sure that all parties that make a reservation will show? b) How many reservations can the owner accept and still be at least 90% sure...
Parents of an 8-year-old boy and an 11-year-old girl want to enroll their children in a...
Parents of an 8-year-old boy and an 11-year-old girl want to enroll their children in a resistance training program at the local community center. They believe that resistance training will help make their children stronger and faster (and maybe even improve their soccer performance), but they are concerned about the potential for injury. Comment on issues regarding the safety of youth resistance training, and highlight program design considerations that address these concerns.
It is known from past information that the probability of failing to finish an Ironman (called...
It is known from past information that the probability of failing to finish an Ironman (called a DNF) is 15%. Suppose we take a sample of 100 Ironman races over the past few years and find that the DNF percentage is 12%. We are interested in seeing if there has been a significant decrease in the number of DNFs. Use alpha=0.05. Find the 95% confidence interval for the percentage of DNFs. a. (0.0665, 0.1735) b. (0.0555, 0.1845) c. (0.1179, 0.1221)...
The manager of a large apartment complex knows from experience that 90 units will be occupied...
The manager of a large apartment complex knows from experience that 90 units will be occupied if the rent is 468 dollars per month. A market survey suggests that, on the average, one additional unit will remain vacant for each 9 dollar increase in rent. Similarly, one additional unit will be occupied for each 9 dollar decrease in rent. What rent should the manager charge to maximize revenue?
Maria is a 6-year-old girl diagnosed with end-stage osteosarcoma. She is one of 11 children to...
Maria is a 6-year-old girl diagnosed with end-stage osteosarcoma. She is one of 11 children to a large Hispanic family. A hospice nurse has been assigned to the family and notices that the patient’s room is filled with multiple family members. Maria has vomited on the bed from side effects of medication. 1. What should the nurse do next? 2. How can the nurse help with spiritual needs of the patient and family? 3. List examples of what constitutes cold...
Suppose it is known from experience that the standard deviation of the weight of 10-ounce packages...
Suppose it is known from experience that the standard deviation of the weight of 10-ounce packages of cookies is 0.20 ounces. To check whether the true average is, on a given day, 10 ounces, employees select a random sample of 36 packages and find that their mean weight is x¯ = 9.45 ounces. Perform a two-tailed z-test on this data, checking at the α = .01 significance level State the null hypothesis in writing and in numbers State the alternative...
6. You can expect most children in the 5-year-old class to exhibit very similar abilities in...
6. You can expect most children in the 5-year-old class to exhibit very similar abilities in their language and physical development (T/F) 8. Objectives and procedures should be aligned with one another (T/F) 14. In a brainstorming group time, the children identify what they know, what they want to know, and how they would like to find out (T/F) 15. Activities within the body of the group time should vary from one day to the next (T/F) 18. One way...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT