Q1) Quality control process at manufacturing plant needs that each lot of finished units be sampled for defective items. 20 units from each lot are inspected. If 5 or more defective units are found, lot is rejected. If a lot is known to contain 10% defective items, find out the probability that lot will be rejected? Accepted?
i) Let Xi's be random sample of size n from population ~N(2,4). How large should n be in order that: p (1.9≤ Xbar ≤ 2.1)≥ 0.99?
ii) To hunt flying insects, bats emit high-frequency sounds and then listen for their echoes. One interesting question is: how far separately are bat and insect when bat first senses that insect is there? Following table lists bat-to-insect detection for 11 catches. Determine the 95% confidence interval for μ, true bat-to-insect detection distance. Is supposition that bat-to-insect detection distances are normally distributed tenable?
|
Catch Number
|
Detection Distance (cm)
|
Catch Number
|
Detection Distance (cm)
|
|
1
|
62
|
7
|
27
|
|
2
|
52
|
8
|
42
|
|
3
|
68
|
9
|
83
|
|
4
|
23
|
10
|
56
|
|
5
|
34
|
11
|
40
|
|
6
|
45
|
|
|