Answer: The 95% confidence interval is approximately (55.57, 58.43)
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Explanation:
At 95% confidence, the z critical value is about z = 1.960 which you find using a table or a calculator.
The sample size is n = 17
The sample mean is xbar = 57
The population standard deviation is sigma = 3
The lower bound of the confidence interval is
L = xbar - z*sigma/sqrt(n)
L = 57 - 1.960*3/sqrt(17)
L = 55.5738905247863
L = 55.57
The upper bound is
U = xbar + z*sigma/sqrt(n)
U = 57 + 1.960*3/sqrt(17)
U = 58.4261094752137
U = 58.43
Therefore the confidence interval (L, U) turns into (55.57, 58.43) which is approximate.
Answer:
Average weight of the bags of potatoes is 3.8 pounds.
Step-by-step explanation:
Given:
Weight of the first bag, 
pounds.
Weight of the second bag is 0.4 pounds less than twice the weight of first bag. This means,
Weight of the third bag is 0.6 pounds more than that of the first bag. This means,
Weight of the fourth bag is 0.3 pounds less than that of the second bag. This means,
Therefore, the average weight of the bags of potatoes is given as the sum of all the weights and then divide the sum by 4. Therefore,
Therefore, average weight of the bags of potatoes is 3.8 pounds.
Step-by-step explanation:
By binomial theorem,
T(r+1) = nCr * a^(r+1) * b^r
Term 4 = 7C3 * (2x)^4 * (-5y)^3 = 35 * (16x^4) * (-125y^3) = -70000x^4y^3.
The probability of getting a red card is 1/2 and the probability of getting a 10 is 4/52. To find the probability of getting both a red card and a 10, multiply the two.
(1/2)(4/52) = 4/104
4/104 = 1/26
Therefore, the probability is 1/26
