I have a homework assignment that is giving me fits Cant fig

I have a homework assignment that is giving me fits. Can’t figure out these 3 problems. 1. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. What is the probability that a random person has an IQ score between 100 and 121? 2. The random variable x is known to be uniformly distributed between 100 and 200 (A). Compute P(x=145) (B). P(110 x 170) 3. Assume a binomial distribution has p = 0.30 and n = 100. Suppose we want to calculate the probability of fewer than 20 successes (A.) What value do we use to compute the desired probability (what is the continuity correction) (B). What is the Z value corresponding to the answer to a. (C). what is the probability of fewer than 20 successes?

Solution

1. let X be the IQ score

X~N(100,15²)

we are to find P[100<X<121]=P[(100-100)/15<(X-100)/15<(121-100)/15]=P[0<Z<1.4] where Z~N(0,1)

                                          =P[Z<1.4]-P[Z<0]=0.919243-0.5=0.419243 [answer]

2. X~U(100,200)

so pdf is f(x)=1/100     100<x<200

A) P[X=145]=0 because for a continuous distribution the probability of taking a particular value is zero

B) P[110<=X<=170]=P[X<=170]-P[X<=110]=(170-100)/100-(110-100)/100=60/100=0.6