Question

a random sample of n=35 is selected from a population with a mean of 69.3 and a standard deviation of 3.8, and the sample mean is calculated.

describe the distribution of the sample mean (type and its 2 parameters)

find that the probability of sample mean is between 66 and 72

find that P of sample mean is >67

Answer 1

Solution :

Given that,

mean = = 69.3

standard deviation = = 3.8

n = 35

= = 69.3

= / n = 3.8 / 35 = 0.6423

P(66 < < 72) = P((66 - 69.3) /0.6423 <( - ) / < (72 - 69.3) / 0.6423))

= P(-5.14 < Z < 4.20)

= P(Z < 4.20) - P(Z < -5.14) Using standard normal table,  

= 1 - 0

= 1

Probability = 1

2)

P( > 67) = 1 - P( < 67)

= 1 - P(( - ) / < (67 - 69.3) / 0.6423)

= 1 - P(z < -3.58)

= 1 - 0.0002 Using standard normal table.

= 0.9998

Probability = 0.9998