A given data value has a Z-value equal to -1.4. Assuming a normal (i.e., symmetr

Question

A given data value has a Z-value equal to -1.4. Assuming a normal (i.e., symmetrical) continuous probability distribution, how many standard deviations is the data value from the mean?

A. cannot be determined

B. 0

C. 1.4

D. -1.4

A given data value has a Z- Value equal to 0. Assuming a normal (i.e., symmetrical) continuous probability distribution, how many standard deviations is the data value from the mean?

A. 0

B. 1

C. 0.5

D. 2

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. Based on a Binomial probability distribution, the probability that less than 2 prefer brand C is ______?

A 0.0102

B. 0.1001

C. 0.0870

D. 0.0768

Suppose that past history shows that 60% of college students prefer Brand C cola. A sample of 5 students is to be selected. Based on a Binomial probability distribution, the probability that at most 2 prefer brand C is ______?

A. 0.3174

B. 0.2304

C. 0.3456

D. 0.4968

E. 0.6890

Explanation / Answer

(1) (D)

A Z-score tells us how many standard deviations the sample data is, away from the mean.

If Z-value is -1.4, this means that data value is -1.4 standard deviations away from the mean.

(2) (A)

If Z = 0, it means that data value = mean, so data value is 0 standard deviations away from mean.

(3) (C)

Let X = event that chosen student prefers brand C.

P(X) = 60% = 0.6

So,

P(X < 2) = P(X = 0) + P(X = 1)

= 5C0 (0.6)0 (0.4)5 + 5C1 (0.6)1 (0.4)4

= 0.01024 + 0.0768 = 0.0870

(4) (A)

Probability that at most 2 students prefer brand C is

P(X <= 2) = P(X = 0) + P(X = 1) + P(X = 2)

= 0.0870 + P(X = 2)

= 0.0870 + 5C2 (0.6)2 (0.4)3

= 0.0870 + 0.2304 = 0.3174

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