Question

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 is at most 119.09 oz? Round your answer to 4 decimal places.

(c) Using your answer to part (a), what is the probability that in a random sample of 14 newborn babies, the mean weight is more than 120.03 oz? Round your answer to 4 decimal places.

Answer 1

Solution :

Given that ,

mean = = 119.54

standard deviation = = 0.67

a) n = 14

= = 119.54

= / n = 0.67 / 14 = 0.1791

b) P( 119.09) = P(( - ) / (119.09 - 119.54) / 0.1791)

= P(z -2.51)

Using z table

= 0.0060

c) P( > 120.03) = 1 - P( < 120.03)

= 1 - P[( - ) / < (120.03 - 119.54) /0.1791 ]

= 1 - P(z < 2.74)

Using z table,    

= 1 - 0.9969

= 0.0031