Question

In: Statistics and Probability

Assume that the amount of time (hours) that young apprentices spend per week on their homework...

Assume that the amount of time (hours) that young apprentices spend per week on their homework in their training program at a major manufacturer is normally distributed with a mean of 12 hours and a standard deviation of 5.

3. If 65 apprentices are selected at random, find the probability that they average more than 12 hours per week on homework.

a. 0.3999 b. 0.6999 c. 0.5000 d. 0.7999

4. If 65 apprentices are selected at random, find the probability that they average between 13 and 15 hours per week on homework.

a. 0.1534 b. 0.2534 c. 0.3333 d. 0.0534

Expert Solution

Solution :

Given that,

mean = = 12

standard deviation = = 5

n = 65

= = 12

= / n = 5 / 65 = 0.62

a) P( > 12) = 1 - P( < 12)

= 1 - P[( - ) / < (12 - 12) /0.62 ]

= 1 - P(z < 0)

Using z table,

= 1 - 0.5000

= 0.5000

correct option is = c

c) P(13 < < 15)

= P[(13 - 12) /0.62 < ( - ) / < (15 - 12) / 0.62)]

= P(1.6129 < Z < 4.8387)

= P(Z < 4.8387) - P(Z < 1.6129)

Using z table,

= 1 - 0.9466

= 0.0534

correct option is = d

orchestra answered 1 year ago

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