Question

In: Statistics and Probability

For a random variable that is normally distributed, with μ = 80 and σ = 10,...

For a random variable that is normally distributed, with μ = 80 and σ = 10, determine the probability that a simple random sample of 25 items will have a mean between 78 and 85?

	a.	83.51%
	b.	15.87%
	c.	99.38%
	d.	84.13%

Expert Solution

Solution :

Given that ,

mean = = 80

standard deviation = =10

n = 25

= 80

= / $\sqrt$ n= 10/ $\sqrt$ 25=2

P(78< <85 ) = P[(78 -80) / 2< ( - ) / < (85-80) / 2)]

= P(-1 < Z < 2.5)

= P(Z <2.5 ) - P(Z <-1 )

Using z table

=0.9938 - 0.1587

=0.8351

=83.51%

orchestra answered 2 years ago

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