Question

It is known that the birth weight of newborn babies in the U.S. has a mean...

  1. It is known that the birth weight of newborn babies in the U.S. has a mean of 7.1 pounds with a standard deviation of 1.5 pounds. Suppose we randomly sample 36 birth certificates from the State Health Department, and record the birth weights of these babies.

  

  1. The sampling distribution of the average birth weights of random samples of 36 babies has a mean equal to ______ pounds and a standard deviation of ______ pounds.


  1. What is the probability the average birth weight of a random sample of 36 babies is less than 7.7 pounds? _______






What is the probability the average birth weight of a random sample of 36 babies is between 6.9 pounds and 7.5 pounds? _______

Homework Answers

Answer #1

Mean of sampling distribution of Sample mean  = = 7.1

Standard deviation of sampling distribution = / sqrt(n) = 1.5 / sqrt(36) = 0.25

Using central limit theorem ,

P( < x) = (Z < (x - ) / ( / sqrt(n) ) )

So,

P( < 7.7) = P(Z < (7.7 - 7.1) / 0.25 )

= P(Z < 2.4)

= 0.9875

P(6.9 < < 7.5) = P( < 7.5) - P( < 6.9)

= P(Z < (7.5 - 7.1) / 0.25) - P(Z < (6.5 - 7.1) / 0.25)

= P(Z < 1.6) - P(Z < -2.4)

= 0.9452 - 0.0082

= 0.9370

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
It is known that the birth weight of newborn babies in the U.S. has a mean...
It is known that the birth weight of newborn babies in the U.S. has a mean of 7.1 pounds with a standard deviation of 1.5 pounds. Suppose we randomly sample 36 birth certificates from the State Health Department, and record the birth weights of these babies. The sampling distribution of the average birth weights of random samples of 36   babies has a mean equal to ______ pounds and a standard deviation of ______ pounds. What is the probability the average...
Statistics Canada reports that the birth weight of newborn babies in Saskatchewan has a mean of...
Statistics Canada reports that the birth weight of newborn babies in Saskatchewan has a mean of 3.45 kg for both sexes. Suppose the standard deviation is 0.7 kg. Further we randomly sample 49 birth certifi- cates in Saskatchewan and record the birth weights of samples babies. Find the mean and standard deviation of the sampling distribution of x ̄. What is the probability that sample mean birth weight will be less than 3.25 kg?
The birth weight of newborn babies is normally distributed with a mean of 7.5 lbs and...
The birth weight of newborn babies is normally distributed with a mean of 7.5 lbs and a standard deviation of 1.2 lbs. a. Find the probability that a randomly selected newborn baby weighs between 5.9 and 8.1 pounds. Round your answer to 4 decimal places. b. How much would a newborn baby have to weigh to be in the top 6% for birth weight? Round your answer to 1 decimal place.
Birth weight, in grams, of newborn babies are normally distributed with a mean of 3290 grams...
Birth weight, in grams, of newborn babies are normally distributed with a mean of 3290 grams and a standard deviation of 520 grams. Find the percentage of newborns that weigh between 3000 and 4000 grams. Consider again the birth weights of newborn babies, where the mean weight is 3290 grams and the standard deviation is 520 grams. Find the weight, in grams, that would separate the smallest 4% of weights of newborns from the rest.
Some sources report that the weights of full-term newborn babies have a mean of 6.5 pounds....
Some sources report that the weights of full-term newborn babies have a mean of 6.5 pounds. A pediatrician believes that the average weight of full-term newborn baby is slightly increased. A random sample of 30 full-term newborn baby is selected with an average weight of 7 pounds and a standard deviation of 0.8 pounds. Conduct the hypothesis test at 5% significance level.
Problem 4 –Weights of newborn babies (6 marks) Paediatricians measure the weights of newborn babies to...
Problem 4 –Weights of newborn babies Paediatricians measure the weights of newborn babies to closely monitor their growth in the first six months of their life. A study reveals that weights of newborn babies are normally distributed with a mean of 3.2kg and a standard deviation of 0.4kg. a) Find the probability that a randomly selected newborn baby would have a weight more than 3.5kg. Display working. 1 mark b) Eight newborn babies are randomly selected. What is the probability...
Suppose that the birth weights of infants are Normally distributed with mean 120 ounces and a...
Suppose that the birth weights of infants are Normally distributed with mean 120 ounces and a standard deviation of 18 ounces. (Note: 1 pound = 16 ounces.) a) Find the probability that a randomly selected infant will weight less than 5 pounds. b) What percent of babies weigh between 8 and 10 pounds at birth? c) How much would a baby have to weigh at birth in order for him to weight in the top 10% of all infants? d)...
Some sources report that the weights of full-term newborn babies in a certain town have a...
Some sources report that the weights of full-term newborn babies in a certain town have a mean of 7 pounds and a standard deviation of 0.6 pounds and are normally distributed. a. What is the probability that one newborn baby will have a weight within 0.6 pounds of the mean is, between 6.4 and 7.6 pounds, or within one standard deviation of the mean? b. What is the probability that the average of four babies' weights will be within 0.6...
A scientist has read that the mean birth weight, ?, of babies born at full term...
A scientist has read that the mean birth weight, ?, of babies born at full term is 7.4 pounds. The scientist, believing that ? is different from this value, plans to perform a statistical test. She selects a random sample of birth weights of babies born at full term and finds the mean of the sample to be 7.1 pounds and the standard deviation to be 1.8 pounds. Based on this information answer the following questions What are the null...
Birth weights of newborn babies follow a normal distribution with mean of 3.39 kg and standard...
Birth weights of newborn babies follow a normal distribution with mean of 3.39 kg and standard deviation of 0.55 kg. Use a table of Z ‑critical values to find the probability that a newborn baby weighs less than 2.125 kg. Give your answer as a percentage rounded to two decimal places. Probability: