Question

In: Math

The birthweight of newborn babies is Normally distributed with a mean of 3.39 kg and a...

The birthweight of newborn babies is Normally distributed with a mean of 3.39 kg and a standard deviation of

0.55 kg.

(a) Find the probability that a baby chosen at random will have a birthweight of over 3.5 kg.

(b) Find the probability that an SRS of 16 babies will have an average birthweight of over 3.5 kg.

(c) Find the probability that an SRS of 100 babies will have an average birthweight of over 3.5 kg.

(d) What range of average birthweights would the largest 15% of samples of size 100 babies have?

Solutions

Expert Solution

Solution :

Given that ,

mean = = 3.39

standard deviation = = 0.55

(a)

P(x > 3.5) = 1 - P(x < 3.5)

= 1 - P((x - ) / < (3.5 - 3.39) / 0.55)

= 1 - P(z < 0.2)

= 1 - 0.5793

= 0.4207

P(x > 3.5) = 0.4207

Probability = 0.4207

(b)

n = 16

= 3.39 and

= / n = 0.55 / 16 = 0.55 / 4 = 0.1375

P( > 3.5) = 1 - P( < 3.5)

= 1 - P(( - ) / < (3.5 - 3.39) / 0.1375)

= 1 - P(z < 0.8)

= 1 - 0.7881

= 0.2119

P( >) = 0.2119

Probability = 0.2119

(c)

n = 100

= 3.39 and

= / n = 0.55 / 100 = 0.55 / 10 = 0.055

P( > 3.5) = 1 - P( < 3.5)

= 1 - P(( - ) / < (3. - 3.39) / 0.055)

= 1 - P(z < 2)

= 1 - 0.9772

= 0.0228

P( > 3.5) = 0.0228

Probability = 0.0228

(d)

P(Z > z) = 1%

1 - P(Z < z) = 0.15

P(Z < z) = 1 - 0.15 = 0.85

P(Z < 1.04) = 0.85

z = 1.04

= z * + = 1.04 * 0.55 + 3.39 = 3.962

Range = 3.96


Related Solutions

Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9...
Suppose that the mean weight of newborn babies is normally distributed with a mean of 6.9 pounds and a standard deviation of 0.8 pound. A developmental psychologist wants to test whether newborn babies of mothers who use drugs during pregnancy differ in weight from the average baby. The psychologist takes a random sample of 30 mothers who used drugs during pregnancy and computes the mean birth weight of these mothers’ babies. This sample of 30 mothers has a sample mean...
The weight of newborn babies are normally distributed with a mean of 7.62 pounds and a...
The weight of newborn babies are normally distributed with a mean of 7.62 pounds and a standard deviation of 0.61 pounds. If the weight of 22 newborn are randomly selected, what's the probability that their mean weight is more than 7.23 pounds? Round to 4-decimal places
The weights for newborn babies is approximately normally distributed with a mean of 5lbs and a...
The weights for newborn babies is approximately normally distributed with a mean of 5lbs and a standard deviation of 1.5lbs. Consider a group of 1,000 newborn babies: How many would you expect to weigh between 4-7lbs? How many would you expect to weigh less than 6lbs? How many would you expect to weigh more than 5lbs? How many would you expect to weigh between 5-10lbs?
Q. The birthweight (denoted by a random variable W )of babies in normally distributed with mean...
Q. The birthweight (denoted by a random variable W )of babies in normally distributed with mean of 3500g and standard deviation 500gm. a) Use and show the manual calculations that determine the birthweight that only 5% of the birthweight would exceed. b) Provide the r commander commands and output to show that the value for part a is correct.
The weights for newborn babies is approximately normally distributed with a mean of 6.9 pounds and...
The weights for newborn babies is approximately normally distributed with a mean of 6.9 pounds and a standard deviation of 1.1 pounds. Consider a group of 1200 newborn babies: 1. How many would you expect to weigh between 6 and 9 pounds? 2. How many would you expect to weigh less than 8 pounds? 3. How many would you expect to weigh more than 7 pounds? 4. How many would you expect to weigh between 6.9 and 10 pounds?
The weights of American newborn babies are normally distributed with a mean of 119.54 oz (...
The weights of American newborn babies are normally distributed with a mean of 119.54 oz ( about 7 pounds 8 ounces) and a population standard deviation of .61 oz. A sample of 11 newborn babies is randomly selected from the population. (a) find the standard error of the sampling distribution. Round your answer to 4 decimal places. (b) Using your answer to part (a), what is the probability that in a random sample of 11 newborn babies, the mean weight...
The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and...
The weights for newborn babies is approximately normally distributed with a mean of 6.4 pounds and a standard deviation of 1.4 pounds. Consider a group of 1100 newborn babies: 1. How many would you expect to weigh between 4 and 8 pounds?  2. How many would you expect to weigh less than 7 pounds?  3. How many would you expect to weigh more than 6 pounds?  4. How many would you expect to weigh between 6.4 and 10 pounds? 
he weights for newborn babies is approximately normally distributed with a mean of 5.1 pounds and...
he weights for newborn babies is approximately normally distributed with a mean of 5.1 pounds and a standard deviation of 1.4 pounds. Consider a group of 1500 newborn babies: 1. How many would you expect to weigh between 3 and 6 pounds? 2. How many would you expect to weigh less than 5 pounds? 3. How many would you expect to weigh more than 4 pounds? 4. How many would you expect to weigh between 5.1 and 8 pounds? Get...
2. The weights of American newborn babies are normally distributed with a mean of 119.54 oz...
2. The weights of American newborn babies are normally distributed with a mean of 119.54 oz (about 7 pounds 8 ounces) and a population standard deviation of 0.67 oz. A sample of 14 newborn babies is randomly selected from the population. (a) Find the standard error of the sampling distribution. Round your answer to 4 decimal places. (b) Using your answer to part (a), what is the probability that in a random sample of 14 newborn babies, the mean weight...
The population of the birthweight of babies at a hospital, has a mean of 112 ounces...
The population of the birthweight of babies at a hospital, has a mean of 112 ounces and a standard deviation of 20.6 ounces. What is probability that a sample of the birthweights of the next 49 babies born at the hospital has a mean of more than 107 ounces. a) .0028 b) .9616 c) .0446 d) .9545
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT