Question

In: Statistics and Probability

Correct the final answers to 4 decimal places whenever appropriate. The score in an test is...

Correct the final answers to 4 decimal places whenever appropriate.

The score in an test is normally distributed with a mean of 590 and a standard deviation of 150. A researcher randomly selected some candidates who took the test. If the score of a candidate is less than 480, the candidate is classified as failing the test.

Find the probability that a randomly selected candidate fails the test.
Find the value of k if there is10% chance that a randomly selected candidate student has a score more thank.
Suppose a random sample of 13 candidates is selected. Find the probability that the mean score of them is over 550.
Suppose a random sample of 7candidatesis selected. Find the probability that at most 2 of them with score less than 524.
Suppose a random sample of 500 candidates is selected. Find the probability that at least 350 of them with score more than 524.

Expert Solution

Given that the score in an test is normally distributed with a mean of 590 and a standard deviation of 150.

a) The probability,

b) We need

c) The probability,

d) The probability,

Now use binomial distribution,

e) Here

Now use binomial distribution,

orchestra answered 3 years ago

Assume that z is the test statistic. (Give your answers correct to two decimal places.) (a)...

Assume that z is the test statistic. (Give your answers correct to two decimal places.) (a) Calculate the value of z for Ho: μ = 10, σ = 2.8, n = 36, x = 11.4. _________ (b) Calculate the value of z for Ho: μ = 120, σ = 26, n = 26, x = 125.9. _________ (c) Calculate the value of z for Ho: μ = 18.2, σ = 4.4, n = 140, x = 18.88. __________ (d) Calculate...

Convert 6∘ to radians, correct to 4 decimal places. 6∘= ____________ rad (4 dec. places). Convert...

Convert 6∘ to radians, correct to 4 decimal places. 6∘= ____________ rad (4 dec. places). Convert 4.75 rad to degrees, correct to 4 decimal places. 4.75 rad = ____________ degrees (4 dec. places). Question b: (2 points) Determine the length of an arc of a circle with radius 6 metres that subtends a central angle of 300∘ to two decimal places. Arc length, s= ____________ m. c A circular wheel of radius 0.55 metres is spinning at a rate of...

Consider the following. (Give your answers correct to two decimal places.) (a) Find the value of...

Consider the following. (Give your answers correct to two decimal places.) (a) Find the value of z(0.22). (b) Find the value of z(0.82).

Consider the following. (Give your answers correct to two decimal places.) (a) Calculate the value for...

Consider the following. (Give your answers correct to two decimal places.) (a) Calculate the value for the test statistic, χ2, for Ho: σ2 = 20.5, n = 16, s2 = 16.5. χ2* = (b) Calculate the value for the test statistic, χ2, for Ho: σ2 = 30.1, n = 22, s = 6.2. χ2* = (c) Calculate the value for the test statistic, χ2, for Ho: σ = 44, n = 22, s = 37.6. χ2* = (d) Calculate the...

Consider the normal curve. (Give your answers correct to four decimal places.) (a) Find the area...

Consider the normal curve. (Give your answers correct to four decimal places.) (a) Find the area to the right of z = 0.00. (b) Find the area to the right of z = 1.28. (c) Find the area to the right of z = -1.67. (d) Find the area to the left of z = 1.46. (e) Find the area to the left of z = -1.46.

Type or paste question hereConsider the following. (Give your answers correct to four decimal places.) (a)...

Type or paste question hereConsider the following. (Give your answers correct to four decimal places.) (a) Find P(0.00 < z < 2.08). (b) Find P(-1.83 < z < 2.09). (c) Find P(z > 0.21). (d) Find P(z < 1.53).

1 x is a binomial random variable. (Give your answers correct to three decimal places.) (a)...

1 x is a binomial random variable. (Give your answers correct to three decimal places.) (a) Calculate the probability of x for: n = 7, x = 3, p = 0.9 P(x) = (b) Calculate the probability of x for: n = 5, x = 4, p = 0.25 P(x) = (c) Calculate the probability of x for: n = 8, x = 2, p = 0.6 P(x) = (d) Calculate the probability of x for: n = 6, x...

1. x is a binomial random variable. (Give your answers correct to three decimal places.) (a)...

1. x is a binomial random variable. (Give your answers correct to three decimal places.) (a) Calculate the probability of x for: n = 1, x = 0, p = 0.35 (b) Calculate the probability of x for: n = 7, x = 6, p = 0.7 (c) Calculate the probability of x for: n = 4, x = 1, p = 0.35 (d) Calculate the probability of x for: n = 3, x = 3, p = 0.7 (e)...

Consider the following. (Give your answers correct to two decimal places.) (a) Find F (15, 30,...

Consider the following. (Give your answers correct to two decimal places.) (a) Find F (15, 30, 0.025). (b) Find F (30, 15, 0.05).

Consider the following. (Give your answers correct to two decimal places.) (a) Find F (10, 3,...

Consider the following. (Give your answers correct to two decimal places.) (a) Find F (10, 3, 0.025). (b) Find F (3, 10, 0.025). You may need to use the appropriate table in Appendix B to answer this question.