Question

Find the probability that an SRS of 36 babies will have an average birthweight of over 3.9 kg. Write your answer as a decimal. Round your answer to two places after the decimal.

Answer 1

Complete question :

The birthweight of newborn babies is Normally distributed with a mean of 3.96 kg and a standard deviation of 0.53 kg. Find the probability that an SRS of 36 babies will have an average birthweight of over 3.9 kg. Write your answer as a decimal. Round your answer to two places after the decimal

Answer:

0.75151

Step-by-step explanation:

Given that :

Mean weight (m) = 3.96kg

Standard deviation (σ) = 0.53kg

Sample size (n) = 36

Probability of average weight over 3.9

P(x > 3.9)

Using the z relation :

Zscore = (x - m) / (σ / √n)

Zscore = (3.9 - 3.96) / (0.53 / √36)

Zscore = - 0.06 / 0.0883333

Zscore = −0.679245

Using the Z probability calculator :

P(Z > - 0.679245) = 0.75151

= 0.75151