Question

In: Statistics and Probability

2] Let x be a continuous random variable that has a normal distribution with μ =...

2] Let x be a continuous random variable that has a normal distribution with μ = 48 and σ = 8 . Assuming n N ≤ 0.05 , find the probability that the sample mean, x ¯ , for a random sample of 16 taken from this population will be between 49.64 and 52.60 .

Round your answer to four decimal places.

Solutions

Expert Solution

Solution :

Given that,

mean = = 48

standard deviation = = 8

n = 16

=   = 48

= / n = 8 / 16 = 2

P(49.64 < < 52.60)  

= P[(49.64 - 48) / 2 < ( - ) / < (52.60 - 48) / 2 )]

= P(0.82 < Z < 2.30)

= P(Z < 2.30) - P(Z < 0.82)

Using z table,  

= 0.9893 - 0.7939

= 0.1954

orchestra answered 2 years ago
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