Question

The distribution of the age, in weeks, at which babies first say "Ma - Ma" is skewed right with mean 50 weeks and standard deviation 2.5 weeks. A random sample of 45 babies is chosen and the age at which each first crawled is recorded.  Is the sampling distribution of the sample mean normally distributed? why

Answer 1

Solution :

Given that ,

mean = = 50

standard deviation = = 2.5

n = 45

sample distribution of sample mean is ,

=

= 50

sampling distribution of standard deviation

=  / n = 2.5 / 45=0.37

= 0.37

here sample size greater than 30 mean normal distribution

and population standard dviation give so we apply sampling distribution