The members of a men’s club have a choice of wearing black or red vests to their club meetings. A study done over a period of many years determined that the percentage of black vests worn is 70%. If there are 10 men at a club meeting on a given night, what is the probability, to the nearest thousandth, that at least 8 of the vests worn will be black?

Step-by-step explanation:

Let x be a random variable representing the number of the members of a men’s club that wear black vests to their club meetings. This is a binomial distribution since the outcomes are two ways. It is either they wear black or red. The probability of success, p = 70/100 = 0.7

The probability of failure, q would be 1 - p = 1 - 0.7 = 0.3

a) Number of samples, n = 10

We want to determine P(x ≤ 8)

From the binomial distribution calculator,

P(x ≤ 8) = 0.851

The probability that at least 8 of the vest worn will be black is 0.75490

Step-by-step explanation:

The parameters given are;

The percentage of black vest worn = 70%, p₀ = 0.7

Number of men in sample, n = 10

Required  number of men who wore black = 8

Proportion of sample = 8/10 = 0.8

The z score of a proportion is given by the relation;

Plugging in the vales, we have;

From the z table we have probability = p(z < 0.69) = 0.75490

The probability that at least 8 of the vest worn will be black = 0.75490.

question 1 is 8, question 2 is 9, question 3 is 24

step-by-step explanation:

now, the numbers they give you at the top are the key. from there, you just have to plug and chug! let's try 1, 2, and 3!

key: a=3, b=5, c=6

1. a+5

remember, a=3, so we plug that in to get 3+5=8

2. 15-c

c=6, so we plug that in to get 15-6=9

3. 4b

b=6, so we plug it in to get 4*6=24

time to try the rest on your own! if you put the answers below in a comment, i'll check them for you!

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!