Question

4. A researcher measures the amount of sugar in several cans of the same soda. The mean is 39.01 with a standard deviation of 0.5. The researcher randomly selects a sample of 100.
a. Find the probability that the sum of the 100 values is greater than 3,909. (Round your answer to four decimal places.)

b. Find the probability that the sum of the 100 values falls between the numbers 3900 and 3910. (Round your answer to four decimal places.

5. An unknown distribution has a mean 12 and a standard deviation of one. A sample size of 25 is taken. Let X = the object of interest.
a. What is the mean of ΣX? (Enter an exact number as an integer, fraction, or decimal.)

b. What is P(Σx < 280)? (Round your answer to five decimal places.)

Answer 1

Answer:

4a)

Given,

Mean = nu

= 100*39.01

= 3901

Standard deviation = sqrt(n) *s

= sqrt(100) * 0.5

= 5

P(X > 3909) = P(z > (3909 - 3901)/5)

= P(z > 1.6)

= 0.0547993 [since from z table]

= 0.0548

b)

P(3900 < X < 3910) = P((3900 - 3901)/5 < (x-u)/s < (3910 - 3901)/5)

= P(-0.2 < z < 1.8)

= P(z < 1.8) - P(z < -0.2)

= 0.9640696 - 0.4207403 [since from z table]

= 0.5433

5.a)

Given,

Mean = 12

Standard deviation = 1

Sample size n = 25

Mean = nu

= 25*12

= 300

standard deviation = sqrt(n) * s

= sqrt(25)*1

= 5

b)

P(x < 280) = P(z < (280 - 300)/5)

= P(z < -4)

= 0.0000317 [since from z table]

= 0.00003