1. A manufacturing process outputs 2% defective items. If a sample of 10 items are selected, calculate the following binomial probabilities.
a. P(X=1 defective)
b. P(X<=1 defective)
2. 65% of attendees at a sales conference are men. If you pick a random sample of 15 attendees,
a. Find the probability of exactly 7 men and 8 women being selected.
b. Find the probability of less than 9 men being selected.
c. Find the probability of no women in the sample.
3. Using a normal distribution having mean of 100 and standard deviation of 7.5, calculate the followinig probabilities:
a. P(X <= 95)
b. P(X >= 110)
c. P(95 <= X <= 105)
4. The lifetimes of certain types of car battery are normally distributed with a mean of 1258 days and a standard deviation of 185 days. If the supplier guarantees them for 1080 days, what proportion of batteries are expected to fail sooner than 1080 days, subject to replacement under the guarantee?
5. Heights of all adult males have a mean of m = 69.0 and standard deviation of s = 2.8, in a normal distribution. Michael Jordan is 78 inches tall. But is his height exceptional compared to the general male population?
a. Calculate the Z-score for Michael Jordan's height.
b. Interpret the meaning of the value you calculated in part a. Is Michael Jordan's height exceptional?
6. A random sample of 50 students has a course averge score of 83 with a standard deviation of 6.1. Using Excel, calculate the confidence interval half width for a 90% confidence interal of the mean score.
7. A tech service hot line call center is concerned about the duration of inbound calls. You have been tasked with compiling and analyzing the center's call data, below, representing a sample of 250 calls from a day's inbound call volume.
a. Calculate the sample mean and standard deviation for call duration time.
b. Calculate a 95% confidence interval for the mean call duration from the sample data.
c. Six months ago, the average call duration was 126. Based on the finding of your confidence interval, is it reasonable to say that call duration has not changed from 6 months ago?
Attachment:- Check Values.rar