Question

A population has a mean of 433 and a standard deviation of 102. If a sample of size 10 is taken, what is the probability the sample mean is greater than 472.2? Enter your answer as a decimal to 3 decimal places

A population has a mean of 218 and a standard deviation of 133. If a sample of size 8 is taken, what is the probability the sample mean is greater than 115.7 but less than 228.8? Enter your answer as a decimal to 3 decimal places.

Answer 1

1)Solution :

Given that ,

mean = = 433

standard deviation = = 102

n = 10

= 433 and

= / n = 102 / 10 = 32.2552

P( > 472.2) = 1 - P( < 472.2)

= 1 - P(( - ) / < (472.2 - 433) / 32.2552)

= 1 - P(z < 1.22)

= 1 - 0.8888 Using standard normal table.

= 0.111

Probability = 0.111

2)Solution :

Given that ,

mean = = 218

standard deviation = = 133

n = 8

= 218 and

= / n = 133 / 8 = 47.0226

P(115.7 < < 228.8) = 1 - P((115.7 - 218) / 47.0226 <( - ) / < (228.8 - 218) /47.0226 ))

= 1 - P(-2.18 < Z < 0.23)

=1 - P(Z < 0.23) - P(Z < -2.18) Using standard normal table,  

= 1 * ( 0.5910 - 0.0146)

= 0.424

Probability = 0.424