A population, with an unknown distribution, has a mean of 80 and a standard deviation of 7. for a sample of 49, the probability that the sample mean will be larger than 82 is

Since the distribution is unknown, we have to think of the CLT (Central Limit Theorem):

n = 49

μ (x) = μ →→ μ (x) = μ = 80

σ (x) = σ / (√v) →→ 7/√49 = 7/7 = 1

Z (x) = (X-μ) / [σ (x) ]

Z (x) = (82-80) / 1

Z (x) = - 2

For Z = - 2, the area (probability) = - 0.0228 (from the left)

and due to symmetry this area is equal in absolute value to the sample larger than 82 (to the right), hence the P (X>82) = 0.228