problem 1) Mine superintendent of ABC Coal Co has recorded the amount of time per work shift that Section Crew A shuts down its machinery for the adjustments, repairs and moving. The records for the crews last 35 shifts are given below;

60     72    126   110    91    115    112
80     66    101    75     93    129    105
113  121    93     87    119    111    97
102  116   114   107    113    119    100
110   99    139   108    128    84      99

(a) Arrange the data in array from highest to lowest.

(b) It is believed that typical amount of downtime per shift is 108 minutes. How many of crew A last 35 shifts exceeded this limit? How many were under the limit?

(c) Construct a relative frequency distribution with 10-minute intervals.

problem 2) John, owner of a Bakery found that average weekly production level of his company was 11,398 loaves, and the variance was 49,729. If date used to find out the results were collected for 32 weeks. During how many weeks was the production level below 11,175? Above 11,844?

problem 3)(a) Two events, A and B are statistically dependent. If

P(A)=0.39, P(B)=0.21, and P(A or B)=0.47

Determine the probability that:

i) Neither A nor B will occur

ii) Both A and B will occur

iii) B will occur, given that A has occurred

iv) A will occur, given that B has occurred.

(b) Given that

P(A)=3/14,    P(B)=1/6, P(C)=1/3,    P(AC)=1/7, and P(B/C)=5/21

Determine the following probabilities: P(A/C), P(C/A), P(BC) and P(C/B)

problem 4) The pressroom supervisor for daily newspaper is being pressured to find ways to print paper closer to distribution time, thus giving the editorial staff more margin for last-minutes changes. She has the option of running the presses at normal speed or at 110 percent of normal “Fast” speed. She estimates that they will run at the higher speed 60 percent of the time. The roll of paper (the newsprint “web”) is twice as likely to tear at the higher speed, which would mean temporarily stopping the presses.

(a) If the web on a randomly selected printing run has a probability of 0.112 of tearing, find the probability that the web will not tear at normal speed?

(b) If the probability of tearing on fast speed is 0.20, find the probability that a randomly selected torn web occurred on normal speed?

problem 5) A company is considering upgrading its computer system, and a main portion of the upgrade is a new operating system. The company has asked the engineer for an evaluation of the operating system. Assume the probability of a favorable evaluation is 0.65. If the probability the company will upgrade its system given a favourable evaluation is 0.85. Find the probability that the company will upgrade and receive favourable evaluation?