Question

In: Statistics and Probability

(a) Use the normal distribution of SAT critical reading scores for which the mean is 513...

(a) Use the normal distribution of SAT critical reading scores for which the mean is 513 and the standard deviation is 112 Assume the variable x is normally distributed.

If 1000 SAT verbal scores are randomly selected, about how many would you expect to be greater than 575?

You would expect that approximately _ SAT verbal scores would be greater than 575 (Round to the nearest whole number as needed.)

(b) The total cholesterol levels of a sample of men aged 35-44 are normally distributed with a mean of 225 milligrams per deciliter and a standard deviation of 37.6 milligrams per deciliter.

If 251 men in the 35-44 age group are randomly selected, about how many would you expect to have a total cholesterol level greater than 251 milligrams per deciliter of blood?

Of the 252 men selected, _ would be expected to have a total cholesterol level greater than 251 milligrams per deciliter of blood. (Round to the nearest integer as needed.)

(c) Use the normal distribution of fish lengths for which the mean is 10 Inches and the standard deviation is 44 inches. Assume the variable x is normally distributed.

If 300 fish are randomly selected, about how many would you expect to be shorter than 66 inches?

You would expect approximately _ fish to be shorter than 6 inches. (Round to the nearest fish.)

Expert Solution

Ans a:

Given,

We convert this to standard normal distribution as

x= = 513, = 112

P(X < x) = P( Z < x - / )

x= SAT verbal scores

P( X > 575) = P( Z > 575 - 513 / 112)

= P( Z > 0.5536)

=1 - P( Z < 0.5536)

= 0.2899

For randomly selected 1000 scores, expected number of scores greater than 575 is

= 0.2899 * 1000

= 289.9

290 (Rounded to nearest integer)

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b) = 225, = 37.6

P(X > 251)

= P(z > (251 - 225)/37.6)

= P(z > 0.69)

= 0.2446

Hence,

1) If 251 men

Expected number = 251*0.2446 =61.39= 61 men

2)If 2512men

Expected number = 252*0.2446 =61.6392= 62 men

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b) = 10, =44

P(X <66)

= P(z < (66-10)/44)

= P(z <1.2728)

= 0.8984

# if 300 fish

Expected number = 300*0.8984 =269.5328= 270 fish

orchestra answered 2 years ago

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