Suppose x has a distribution with μ = 10 and σ = 9. (a) if a random sample of size n = 43 is drawn, find μx, σ x and p(10 ≤ x ≤ 12). (round σx to two decimal places and the probability to four decimal places.)

The probability that P(10 ≤ x ≤ 12). is 42.79%.

The z score is used to determine by how many standard deviations, the raw score is above or below the mean. The z score is given by:

From the normal distribution table, P(10 ≤ x ≤ 12) = P(0 ≤ z ≤ 1.46) = P(z < 1.46) - P(z<0) = 0.9279 - 0.5 = 42.79%.

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P(10 ≤ x ≤ 12) = 0.4274

Step-by-step explanation:

Population mean = u = 10

Population Standard Deviation = = 9

Sample size = n = 43

Sample mean() is equal to the population mean. So,

Sample mean = = 10

Sample standard deviation() is equal to population standard deviation divided by square root of sample size. So,

Sample standard deviation = =

We have to find the probability that for a random sample of n = 43, the value lies between 10 and 12 i.e. P(10 ≤ x ≤ 12)

P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10)

We can find P(x ≤ 12 ) and P(x ≤ 10) by converting these values to z scores.

The formula for z score is:

For x =12, we get:

For x =10, we get:

So,

P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.457) - P(z ≤ 0)

From the z table,

P(z ≤ 1.457) = 0.9274

P(z ≤ 0) = 0.5

So,

P(x ≤ 12) - P( x ≤ 10) = P(z ≤ 1.458) - P(z ≤ 0) = 0.9274 - 0.5 = 0.4274

So,

P(10 ≤ x ≤ 12) = P(x ≤ 12) - P( x ≤ 10) = 0.4274

Therefore,

The probability that for a random sample of size 43, the mean lies between 10 and 12 is 0.4274.

144 p

Step-by-step explanation:

It was due to be returned on 26 November but she returned it on 12 December.

She was therefore with it for an extra 16 days.

The fine is 9p per day. Therefore, she will pay a fine of:

9 * 16 = 144 p