Question

In: Statistics and Probability

1) A normal population has a mean of 100 and a standard deviation of 10. You...

1)

A normal population has a mean of 100 and a standard deviation of 10. You select a random sample of 25. What is the probability that the sample mean calculated will be between 98 and 101?

a.

0.5328
b.

0.3413
c.

.0273
d.

0.682

2)

A normal population has a mean of 100 and a standard deviation of 10. You select a random sample of 25. What is the probability that the sample mean calculated will be less than 98?

a.

.25
b.

0.1915
c.

.1587
d.

0.3413

A normal population has a mean of 100 and a standard deviation of 10. You select a random sample of 25. What is the probability that the sample mean will be greater than 101?

a.

0.3085
b.

0.1915
c.

.25
d.

0.5

Solutions

Expert Solution

Solution :

= / n = 10 / 25 = 2

1)

= P[(98 - 100) / 2< ( - ) / < (101 - 100) / 2)]

= P(-1 < Z < 0.5)

= P(Z < 0.5) - P(Z < -1)

= 0.6915 - 0.1587

= 0.5328

Probability = 0.5328

option a. is correct

2)

P( < 98) = P(( - ) / < (98 - 100) / 2)   

P(z < -1)

= 0.1587

Probability = 0.1587

option c. is correct

3)

P( > 101) = 1 - P( < 101)

= 1 - P[( - ) / < (101 - 100) / 2]

= 1 - P(z < 0.5)

= 1 - 0.6915

= 0.3085

Probability = 0.3085

option a. is correct

orchestra answered 2 years ago
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