Question

A certain species of snake is known to have a mean length of 18.2 inches with a standard deviation of 4.7 inches. Consider repeatedly choosing samples of 50 snakes of this species and finding the mean length of each sample.

a)What is the mean of this sampling distribution of x?

b)What is the standard deviation of this sampling distribution of x?

c)What is the shape of this sampling distribution? Explain how you know this.

d)Find the probability that the mean length for a sample of 50 snakes of this species is more than 20 inches

Show all work on paper.

Answer 1

Solution :

Given that ,

mean = = 18.2

standard deviation = = 4.7

n = 50

a

sample distribution of sample mean is ,

=

= 18.2

b

sampling distribution of standard deviation

=  / n = 4.7/ 50=0.66

= 0.66

c.

sample size greater than 30 n>30 normal distribution

shape of distribution is normal

d.

P( > 20) = 1 - P( < 20)

= 1 - P[( - ) / < (20-18.2) /0.66 ]

= 1 - P(z <2.73 )

Using z table

= 1 - 0.9968

= 0.0032

probability= 0.0032