Question

The scores on a standardized math test for 8th grade children form a normal distribution with a mean of 80 and a standard deviation of 12. (8 points)

a) What is the probability of obtaining a sample mean greater than 82 for a sample of n = 36?

b) What is the probability of obtaining a sample mean less than 78 for a sample of n = 9?

Answer 1

SOLUTION:

From given data,

The scores on a standardized math test for 8th grade children form a normal distribution with a mean of 80 and a standard deviation of 12. (8 points)

Where,

mean = = 80

standard deviation = = 12

a) What is the probability of obtaining a sample mean greater than 82 for a sample of n = 36?

Where,

n = 36

= = 80

= / sqrt(n) = 12/sqrt(36) = 2

Z = ( - )/ = ( - 80 )/ 2

P( > 82) = P(( - )/ > (82 - 80 )/ 2)

P( > 82) = 1 - P(Z < 2/ 2)

P( > 82) = 1 - P(Z < 1)

P( > 82) = 1 - 0.84134

P( > 82) = 0.15866

The probability of obtaining a sample mean greater than 82 for a sample of n = 36 is 0.15866

b) What is the probability of obtaining a sample mean less than 78 for a sample of n = 9?

n = 9

= = 80

= / sqrt(n) = 12/sqrt(9) = 4

P( < 78) = P(( - )/ < (78 - 80 )/ 2)

P( < 78) = P(Z < -2/ 2)

P( < 78) =P(Z < -1)

P( < 78)=0.15866

The probability of obtaining a sample mean less than 78 for a sample of n = 9 is 0.15866