A jeweler had a fixed amount of gold to make bracelets and necklaces. The amount of gold in each bracelet is 6 grams and the amo
1 answer:
Let x represent number of bracelets and y represent number of necklaces.
We have been given that a jeweler made 7 more necklaces than bracelets. This means that number of necklaces will be . We can represent this information in an equation as:
We have been given that the amount of gold in each bracelet is 6 grams, so amount used for x bracelets would be grams.
We are also told that the amount of gold in each necklace is 16 grams, so amount used for y necklaces would be grams.
Since the jeweler used 178 grams of gold, so we will equate the amount of gold used in x bracelets and y necklaces with 178 as:
Therefore, our required system of equations would be:
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Answer:
95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].
Step-by-step explanation:
We are given that a pharmaceutical company proposes a new drug treatment for alleviating symptoms of PMS (premenstrual syndrome).
In the first stages of a clinical trial, it was successful for 7 out of the 14 women.
Firstly, the pivotal quantity for 95% confidence interval for the true proportion is given by;
P.Q. = ~ N(0,1)
where, = sample proportion of women who find success with this new treatment =
= 0.50
n = sample of women = 14
<em>Here for constructing 95% confidence interval we have used One-sample z proportion statistics.</em>
So, 95% confidence interval for the true proportion, p is ;
P(-1.96 < N(0,1) < 1.96) = 0.95 {As the critical value of z at 2.5%
level of significance are -1.96 & 1.96}
P(-1.96 < < 1.96) = 0.95
P( <
<
) = 0.95
P( < p <
) = 0.95
<u />
<u>95% confidence interval for p</u> = [ ,
]
= [ ,
]
= [0.238 , 0.762]
Therefore, 95% confidence interval for p, the true proportion of all women who will find success with this new treatment is [0.238 , 0.762].